Question

Find f”(x)=(3x^4+2)^5

Answer 1

Answer:

180x²(3x⁴+2)⁴+240x³(3x⁴+2)³

Step-by-step explanation:

we need to break this up using the chain rule

(3x⁴+2)=u

so we have

So now we take 3x⁴+2 and take the derivative (which I will assume you know how to do, if not lmk)

which is 12x³

we now need to take the derivative of u⁵=5u⁴

Mulitply these together

60x³u⁴=60x³(3x⁴+2)⁴

do the same thing again

60x³u⁴

we now need to do the mulitplication rleu

(60x³)'(u⁴)+(60x³)(u⁴)'

=

180x²u⁴+60x³*4u³

simplify

180x²(3x⁴+2)⁴+240x³(3x⁴+2)³

while you could do more to simplify it, it would get really messy