QuestionMay 4, 2026

Find f'(x) f(x)=(2-4x)^15 f'(x)= square

Find f'(x) f(x)=(2-4x)^15 f'(x)= square
Find f'(x)
f(x)=(2-4x)^15
f'(x)= square

Solution
3.3(290 votes)

Answer

f'(x) = -60(2 - 4x)^{14} Explanation 1. Apply chain rule For f(x) = (2 - 4x)^{15}, the derivative is f'(x) = 15(2 - 4x)^{14} \cdot \frac{d}{dx}(2 - 4x). 2. Differentiate inner function \frac{d}{dx}(2 - 4x) = -4. 3. Multiply results f'(x) = 15(2 - 4x)^{14} \cdot (-4) = -60(2 - 4x)^{14}.

Explanation

1. Apply chain rule <br /> For $f(x) = (2 - 4x)^{15}$, the derivative is $f'(x) = 15(2 - 4x)^{14} \cdot \frac{d}{dx}(2 - 4x)$. <br />2. Differentiate inner function <br /> $\frac{d}{dx}(2 - 4x) = -4$. <br />3. Multiply results <br /> $f'(x) = 15(2 - 4x)^{14} \cdot (-4) = -60(2 - 4x)^{14}$.
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