Question #89a1e

Question

Question #89a1e

1 Answer

Impact of this question

2827 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-27T19:43:17

$\frac{d y}{d x} = - 6 x^{2} sin (x^{3}) cos (x^{3})$ $(dy)/(dx)=-6x^2sin(x^3)cos(x^3)$

Explanation:

$\frac{d}{d x} {cos}^{2} (x^{3})$ $d/(dx)cos^2(x^3)$

We have to apply chain rule, where $u = cos (x^{3})$ $u=cos(x^3)$

$\frac{d y}{d u} = \frac{d}{d u} u^{2} = 2 u = 2 cos (x^{3})$ $(dy)/(du)=d/(du)u^2=2u=2cos(x^3)$

$\frac{d u}{d x} = \frac{d}{d x} cos (x^{3}) = - 3 x^{2} sin (x^{3})$ $(du)/(dx)=d/(dx)cos(x^3)=-3x^2sin(x^3)$

$\frac{d y}{d x} = \frac{d y}{d u} \cdot \frac{d u}{d x} = 2 cos (x^{3}) \cdot - 3 x^{2} sin (x^{3})$ $(dy)/(dx)=(dy)/(du)*(du)/(dx)=2cos(x^3)*-3x^2sin(x^3)$

$= - 6 x^{2} sin (x^{3}) cos (x^{3})$ $=-6x^2sin(x^3)cos(x^3)$

Science

Math

Humanities

... and beyond

Question #89a1e

1 Answer

Explanation:

Related questions

Impact of this question