I NEED HELP: Find the derivative of the function.
F(x) = (x^4 + 3x^2 − 6)^4

Question

I NEED HELP: Find the derivative of the function.
F(x) = (x^4 + 3x^2 − 6)^4

anonymous · Answer

You must use Chain Rule.

$$g(x) = x^4 + 3x^2 - 6$$When you have:$$F(x) = f(g(x))$$$$F'(x) = f'(g(x))*g'(x)$$in this case:$$f(x) = x^4$$$$g(x) = x^3 + 3x^2 - 6$$$$f(g(x)) = (x^3 + 3x^2 - 6)^4$$

when i do this, i see it as, derivative of whole thing times the derivative of what's inside.

$$F'(x) = f'(g(x)) = 4(x^4 + 3x^2 -6)^3 * (4x^3 + 6x)$$
usually no need to simplify further

anonymous · Answer

please ignore second line and typo for what g(x) is. we both know what it really is ^_^

anonymous · Answer

and the second to last line, after the first equality,lol.

but the final answer is right

and the initial F'(x) = f'(g(x))*g'(x)

is this helpful? any questions?