Question

Find the derivative of the function. But don't simplify the answer

Answer 1

\[f(x)= (5x^3+3x^2-7x)^{7.5}\]

Answer 2

Chain rule is used right?

Answer 3

yes

Answer 4

i dont know how to do that

Answer 5

(derivative of outside) x (derivative of inside) x (derivative of inside inside ) x (derivative of inside inside inside... )

Answer 6

nom sayin?

Answer 7

the answer will be \[7.5(15x^2+6x-7)(5x^3+3x^2-7x)^{8.5}\]

Answer 8

Am i correct?

Answer 9

not quite

Answer 10

there's only 2 layers, so it should only be the derivative outside multiplied by the derivative inside

Answer 11

and you're supposed to subtract the exponent by 1, not add 1.

Answer 12

i dont understand.

Answer 13

the exponent will be 6.5

Answer 14

if f(x) = a^7.5

then f'(x) = 7.5a^6.5 x (derivative of a)

bring the exponent down and subtract it by one.

Answer 15

nom sayin?

Answer 16

i get the exponent. I dont understand the derivative inside outside thing that you said

Answer 17

treat the stuff inside the bracket as another function

then f(x) = [f(g)]^7.5
then f'(x) = 7.5 [f(g)] ^6.5 x f'(g)

the exponent is multiplied by the function and subtracted by one

Answer 18

nom sayin?

Answer 19

7.5(5x^3+3x^2-7x)^6.5x(15x^2+6x-7)

Answer 20

??

Answer 21

yes.