What is the derivative of #y = sin(tan(5x))#?

1 Answer
mason m
Dec 16, 2015

#y'=5sec^2(5x)cos(tan(5x))#

Explanation:

Use the chain rule. The first overriding issue is the tangent function inside the sine function.

#y'=cos(tan(5x))d/dx[tan(5x)]#

Next, use chain rule again to find the derivative of the tangent function.

#d/dx[tan(5x)]=sec^2 5xd/dx[5x]=5sec^2(5x)#

Multiply this back in to find #y'#.

#y'=5sec^2(5x)cos(tan(5x))#

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