Question

Find the Derivative:

Answer 1

\[y=\frac{3}{(5x^2+\sin2x)^{3/2}}\]

Answer 2

\(\bf \Large y=\frac{3}{(5x^2+\sin2x)^{\frac{3}{2}}} \implies
y = 3 \times (5x^2+\sin2x)^{-\frac{3}{2}}\)

Answer 3

So I end up with this:
\[y'=3*\frac{-3}{2}(5x^3+\sin2x)^{-1/2}*10x+2\cos2x\]
Unsimplified, right?

Answer 4

yeah, I'd leave it unsimplified

Answer 5

Alright thank you!

Answer 6

yw

Answer 7

though I left it as \(\bf\Large -\cfrac{9}{2}\left(5x^2+sin(2x)\right)^{-\frac{5}{2}}\)

Answer 8

use the quotient rule...$$y=3(5x^2+\sin2x)^{-3/2}\\y'=3\times-3/2~(5x^2+\sin2x)^{-5/2}(10x+2\cos2x)=-\frac{9(10x+2\cos2x)}{2(5x^2+\sin2x)^{5/2}}$$

Answer 9

Darn, I'm confusing myself with integrals..