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2 votes
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

User Vlad Preda
by
7.2k points

2 Answers

3 votes

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.



User Alex Vergara
by
8.6k points
3 votes

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


User Felixqk
by
7.7k points

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