Need help to simplify the derivative

Question

Can someone tell me what would be the output of this equation? $$\frac{d}{dx}[\cos^4(x)\cdot\cos (x^4)] = -4x^3\cdot\cos^4(x)\cdot\sin (x^4)+4\cos(x^4)\cdot\cos^3(x)\cdot\sin(x)$$

But am not getting the same answer, would like to know what would be the answer? Could you please derive and show me?

Thanks,
-Kamal.

the second term should have a negative sign too; not a plus sign as you have it. — abel, Mar 05 '15 at 05:51
I removed the tag "differential equations" because this is not a differential equation — Dylan, Mar 07 '15 at 01:37

score 1 · Accepted Answer · answered Mar 05 '15 at 06:53

1

Use product rule to find: $$ \dfrac{d}{dx}\left[ \cos^4(x)\cdot \cos(x^4)\right]=\cos(x^4)\dfrac{d}{dx}\cos^4(x)+\cos^4(x)\dfrac{d}{dx}\cos(x^4) $$ than chain rule gives $$ = -4\cos^3(x)\cdot\sin(x)\cdot\cos(x^4)-4x^3\sin(x^4)\cdot\cos^4(x) $$

answered Mar 05 '15 at 06:53

Emilio Novati

62,675

This is exactly the answer I got, thanks bad textbook. – Kamal Mar 05 '15 at 08:32

Need help to simplify the derivative

1 Answers1