Question

Find f '(−4), if f(x) = (5x^2 + 6x)(3x^2 + 7)
I don't just want an answer i would really like an explanation and help doing this, derivatives are confusing me gravely

Answer 1

do you know the "product rule" ?

Answer 2

to do this problem, you "break it down" into a bunch of simpler problems.
the first step is write down the product rule for taking a derivative.
for example, see https://www.khanacademy.org/math/differential-calculus/taking-derivatives/product_rule/v/product-rule
for background

Answer 3

you can expand actually... or at least I would do so.
Then differentiate the function (i.e. take the derivative).
And then, plug in -4 for x, into the derivative of the function.

Answer 4

Sorry you guys i kinda forgot that i posted it.. so do i do the derivative of 5x^2+6x which is 10x+6 and then the derivative of 3x^2+7 which is just 6x and then plug in negative 4 for both of those and get -34 times -24 and just leave the answer at 816? @SolomonZelman @phi

Answer 5

it's a little more complicated:
d( u * v) = u dv + v du
with u= 5x^2+6x, du= 10x+6 (as you posted)
and v= 3x^2+7, dv = 6x
now put the pieces together:
u dv becomes (5x^2+6x)*6x
v du is (3x^2+7)*(10x+6)
and the derivative is
6x(5x^2+6x) + (3x^2+7)(10x+6)

rather than multiply and combine like terms to get a simplified expression I would sub in x=-4 and evaluate.