Question

If f(x) = (5x^3 − 4)^4, then what is f '(x)?

a. 20x^2(x^3 − 4)^3
b. 20x^8
c. 4(5x^3 − 4)^3(15x^2)
d. 4(2x^3 − 4)^4

Answer 1

f(x) = (5x^3 − 4)^4

f'(x) = 4(5x^3 - 4)d(5x^3 -4)/dx

= 4(5x^3 - 4)(5*3x^2)

= 4(5x^3 - 4)(15x^2)

so ans is c.

Answer 2

If f(x) = (5x^3 − 4)^4

derivative of the outer * derivative of the inner

f'(x) = 4 (5x^3 -4) ^3 *3 (5x^2)

= 4 (5x^3 -4) ^3 * (15x^2)

=4*3*5 x^2 (5x^3 -4) ^3

=60 x^2 *(5x^3 -4) ^3

Choice C