The first-order derivative of function f(x) = (3x⁵ + 6)⁵ with respect to x is?
- (3x⁵ + 6)⁴(75x⁴ + 30)
- (3x⁵ + 6)⁴(75x⁴)
- 5(3x⁵ + 6)⁴
- None of these
Explanation
Calculating the Derivative
Given: f(x) = (3x^5 + 6)^5
Using the chain rule: f'(x) = 5(3x^5 + 6)^4 . d/dx(3x^5 + 6)
= 5(3x^5 + 6)^4 . 15x^4
= 75x^4(3x^5 + 6)^4
= (3x^5 + 6)^4 . 75x^4
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