Question

Derivtative of sin^2 (x)^5?
Confused..help please..

Answer 1

is this correct?
\[\sin^2(x^5)\]

Answer 2

or \[[\sin^2(x)]^5\]

Answer 3

first one

Answer 4

You use chain rule. So derivative of the outside times derivative of the inside.

Answer 5

\[\LARGE \cos^2(x^5) \times 2\cos(x)^5 \times 5x^4\]
this is wrong? :?

Answer 6

first sine...then sine(square) then x^5

Answer 7

Your outside would be \[\sin^2(u)\]
where: \[u=x^5\]

Answer 8

\[2\sin(x^5) \times \cos(x^5) \times 5x^4\]

Answer 9

Notice how I went from outside to inside? It's like saying \[[\sin(x)]^2\]

Answer 10

my next step was to take the derivative of the inside, which is INSIDE the brackets. Which was the sine\[\sin^2([x^5])\]
then I went MORE inside after i took the derivative:
\[x^5\]

Do you see the pattern?

Answer 11

why did we differentiate 2 first and not sine?like i did?i tried to do the same thing.

Answer 12

i went from outside>inside too