Question

f(x) = sin(sinx^3)
f'(x) = ?

Answer 1

Have you learn chain rule yet?

Answer 2

how did you know it was chain rule and not the product rule ?

Answer 3

chain rule!

Answer 4

composition of functions uses chain rule
multiplication of functions uses the product rule

Answer 5

Because you have a composition of function instead of multiplication. If you have \(f(x)g(x)\), then use product rule. If you have \(f(g(x))\), use chain rule instead.

Answer 6

cos(sinx^3)(3cosx^2) ?

Answer 7

\[\begin{split}
d(\sin(\sin(x^3))) &= \cos(\sin(x^3))d(\sin(x^2)) \\
&= \cos(\sin(x^3))\cos(x^3)d(x^3) \\
&= \cos(\sin(x^3))\cos(x^3)3x^2dx
\end{split}
\]

Answer 8

oh pellet.

Answer 9

thanks <3

Answer 10

It is interesting how sh!t becomes "pellet".

Answer 11

Lol yea