How do you use the chain rule to differentiate #y=7/(2x+7)^2#?

1 Answer
mason m
Mar 13, 2017

#dy/dx=(-28)/(2x+7)^3#

Explanation:

The derivative of #x^-2# is #-2x^-3#, through the power rule.

When we have a function to the negative second, we take its derivative the same way, but then multiply that by the derivative of the inner function through the chain rule. That is, the derivative of #(f(x))^-2# is, through the chain rule, #-2(f(x))^-3*f'(x)#.

This said, we have:

#y=7(2x+7)^-2#

So its derivative is:

#dy/dx=7(-2(2x+7)^-3)*d/dx(2x+7)#

Don't forget to multiply by the derivative of #2x+7#, which is #2#.

#dy/dx=-28(2x+7)^-3#

#dy/dx=(-28)/(2x+7)^3#

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