Question

What's the 2nd derivative of f(x)=5(2-7x)^4? Explain how to do it via the Chain Rule.

Answer 1

You have to apply the chain rule.

[f(g(x))]' = f'(g(x)) * g'(x)

so (3x + 5) ^2 you would have f(x) = x^2 and g(x) = 3x + 5. f'(x) = 2x, g'(x) = 3 so you would get 2(3x+5) * 3.

Answer 2

@Loser66 @jim_thompson5910

Answer 3

Find y' then find y''

Answer 4

I'll tell you the first derivative can you find the second?

Answer 5

f'(x) = 140(7x-2)^3

Answer 6

Now use this as a guideline, I suggest you figure out how I got that then work on f''(x)

Answer 7

Just keep it as -140(2-7x)^3
No need to be messing with that negative out front.

Answer 8

@Psymon @Loser66 no, how do I do it via the Chain Rule?

Answer 9

To get the first derivative you have to use chainrule, that's where you take the exponent and multiply it by the "5", exponent rule really then you have to find the derivative of the composition, and then -1 so your first step would be...20(2-7x)^3*(2-7)'

Answer 10

2nd derivative is found the same way.

Answer 11

Did you get it?