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Find the derivative of the function y=(2x+5)^4(3x+1)^-5

Find the derivative of the function y=(2x+5)^4(3x+1)^-5

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.3: The Chain Rule
Problem 6YT
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Question

Find the derivative of the function

y=(2x+5)^4(3x+1)^-5
Expert Solution
Step 1

The given function is y=(2x+5)4(3x+1)-5.

The negative property of exponent isa-x is 1ax.

The quotient rule of derivative states that ddxf(x)g(x)=g(x)f'(x)-f(x)g'(x)g(x)2, where f(x) and g(x) are differentiable function.

The sum rule of derivative states that ddxf(x)+g(x)=f'(x)+g'(x), where f(x) and g(x) are differentiable function.

The chain rule of derivative states that ddxfg(x)=f'(g(x))g'(x), where f(x) and g(x) are differentiable function.

The derivative of a constant is zero.

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