Question

Find the derivative of the function.

y = (5x - 4)^4(8x^2 - 5)^-3

Answer 1

use chain rule twice.

Answer 2

Also, product rule. :)

Answer 3

Or if you wanna go nuts, you can use the quotient rule as well:

\[y = \frac{(5x-4)^4}{(8x^2-5)^3}\]

Answer 4

do you understand that?

Answer 5

nope

Answer 6

chain rule:
first, you take derivative of (5x-4)^4 = 4(5x-4)^3
multiply by derivative of (5x): 5
no change to second multiplier

second step - first multiplier with no change * derivative of
(8x^2-5)^(-3) : -3*(8x^2-5)^(-4)
multiplied by derivative of (8x^2): 16x

Answer 7

will give you:
y'=4*5*(5x-4)^3 *(8x^2-5) -(5x-4)^4 *3*16x*(8x^2-5)^(-4)
simplify

Answer 8

try to do it yourself on paper & let me know

Answer 9

ok