Question

f(x) = 21x^16e^-36x
find f'(x)

Answer 1

Product rule, chain rule, rule for derivative of polynomials, rule for derivative of exponential functions. Try it yourself, then we'll give you feedback.

Answer 2

do i start with \[21x^{16}\] d/dx \[e ^{-36x}\] + \[e ^{-36x}\] d/dx \[21x^{16}\]

Answer 3

i dont know how to solve this

Answer 4

is that right?

Answer 5

This function is the product of two other functions, times a constant. Recall a few rules:\[\frac{d(kf)}{dx}=k \frac{df}{dx}\]The derivative of a constant times a function is the constant times the derivative of the function.

Answer 6

You are on the right track. Keep going. You need to figure the derivatives in your diagram now.

Answer 7

Am i doing it right?

Answer 8

\[f(x) = 21x^{16}e^{-36x }\]\[f(x) = 21(16x^{15}e^{-36x }+x^{16}(-36)e^{-36x})\]Product rule and chain rule.

Answer 9

I think so; just needs some gathering of constants (multiply to get a single constant per term). Nice work.

Answer 10

i dont know how to do the next steps

Answer 11

I think you're just about done here. All that is left is to multiply the constants.

Answer 12

thank you

Answer 13

\[f(x)=21(16x^{15}e^{−36x}+x^{16}(−36)e^{−36x})=336x^{15}e^{−36x}-756x^{16}e^{−36x}\]

Answer 14

Got it?