digraph physicsDerivation { 
overlap = false;
label="derivation: identity sin(2 x) = 2 sin(x) cos(x) using Euler's equation
https://allofphysiscs.com";
fontsize=12;
0005887774 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0005887774 -> generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80;
generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80.png",labelloc=b];
0006240603 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_changevariableXtoY.png",labelloc=b];
generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80 -> 0006240603;
generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80.png",labelloc=b];
0006240603 -> generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539;
generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539.png",labelloc=b];
generated_feed_9110536742_13cba4214eaa8800b46b93469e358ea75d104eaa4c9688c48054faa609db05cb -> 0006240603;
generated_feed_9110536742_13cba4214eaa8800b46b93469e358ea75d104eaa4c9688c48054faa609db05cb [shape=box, color=red,label="",image="/code/static/generated_feed_9110536742_13cba4214eaa8800b46b93469e358ea75d104eaa4c9688c48054faa609db05cb.png",labelloc=b];
generated_feed_4961662865_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 -> 0006240603;
generated_feed_4961662865_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881 [shape=box, color=red,label="",image="/code/static/generated_feed_4961662865_2d711642b726b04401627ca9fbac32f5c8530fb1903cc4db02258717921a4881.png",labelloc=b];
0006131891 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declareinitialexpression.png",labelloc=b];
0006131891 -> generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96;
generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96.png",labelloc=b];
0001541045 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_multiplyexpr1byexpr2.png",labelloc=b];
generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96 -> 0001541045;
generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_4585932229_227c92a24bba6e0031f7623c2faaa72a95fb3d5657e6d6d7b26c688f8de98b96.png",labelloc=b];
generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80 -> 0001541045;
generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2103023049_7b718eec75182e669421b98e865fdafb5a6619b6257df153f3e68df4802d1b80.png",labelloc=b];
0001541045 -> generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62;
generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62.png",labelloc=b];
0008636739 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_multiplybothsidesby.png",labelloc=b];
generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62 -> 0008636739;
generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_3470587782_a4794b852d5ff7662edea113dc480e94509ab13dd565bbe1c2978bb9d93ffe62.png",labelloc=b];
0008636739 -> generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f;
generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f.png",labelloc=b];
generated_feed_8642992037_d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35 -> 0008636739;
generated_feed_8642992037_d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35 [shape=box, color=red,label="",image="/code/static/generated_feed_8642992037_d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35.png",labelloc=b];
0009916897 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_simplify.png",labelloc=b];
generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f -> 0009916897;
generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9894826550_fe2811140cf7e37261729a7bbb0eaf0f2bbf723014e4067cd563cb998400830f.png",labelloc=b];
0009916897 -> generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb;
generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb.png",labelloc=b];
0006790653 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_simplify.png",labelloc=b];
generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb -> 0006790653;
generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8699789241_faed5ed6848caa4c0927e026fb0bff4461764a3d5aad54300533db2cb0cdf2bb.png",labelloc=b];
0006790653 -> generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40;
generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40.png",labelloc=b];
0002750343 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_RHSofexpr1equalsRHSofexpr2.png",labelloc=b];
generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539 -> 0002750343;
generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_8483686863_dcf022e72bb842208e61b2f0daffc71a87330d107fbf745fa29fc6816d8c7539.png",labelloc=b];
generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40 -> 0002750343;
generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40 [shape=ellipse, color=black,label="",image="/code/static/generated_expression_9180861128_67570d72dce3054e379823603f9791beed73ca946b54ee598e72253d5323df40.png",labelloc=b];
0002750343 -> generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e;
generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e.png",labelloc=b];
0007763037 [shape=invtrapezium, color=blue, label="",image="/code/static/generated_declarefinalexpression.png",labelloc=b];
generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e -> 0007763037;
generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e [shape=ellipse, color=black,label="",image="/code/static/generated_expression_2405307372_41fa61a408fb63d7241ca9992e6657c92927242fbae1b53f2ae734e7f28e147e.png",labelloc=b];
}