Question

derivative of sin^2(x^2 +2)?

Answer 1

use chain rule

Answer 2

cos^2x(x^2+2)(2x) right?

Answer 3

no
2sin(x^2+2)cos(x^2+2)(2x)

Answer 4

how come?

Answer 5

let ^2 be f
let sin be g
let x^2+2 be h, then
d[f(g(h))]/dx = f'g'h'

Answer 6

...?

Answer 7

so 3 inside each other? how would...? what.

Answer 8

nvmind I will figure out tomorrow

Answer 9

that's chain rule

Answer 10

Let \[f(x)=x^2, g(x)=sinx, h(x)=x^2+2\]
Then,\[\sin^2(x^2+2)=f(g(h(x)))\]
Chain Rule, which is one of the ways to compute derivative is follows.\[a(b(x))'=a'(b(x))*b'(x)\]
Applying chain rule twice for our problem makes it\[f(g(h(x)))'=f'(g(h(x)))*(g(h(x)))'=f'(g(h(x)))*[g'(h(x))*h'(x)]\]
which is,\[4xsin(x^2+2)\cos(x^2+2)\]