Find the derivative of y=tan sqrt{3x-1} (see equation in details) using chain rule?

#y=tan\sqrt{3x-1}#

1 Answer
Fleur
Feb 8, 2018

#dy/dx =(3 sec^2 sqrt(3x-1) )/ (2 sqrt (3x-1))#

Explanation:

The Chain Rule: #(f @ g)' (x) = f'(g(x)) * g'(x)#

First differentiate the outside function, leaving the inside alone, and then multiply by the derivative of inside function.

#y = tan sqrt(3x-1)#

#dy/dx = sec^2 sqrt(3x-1) * d/dx sqrt(3x-1)#

#= sec^2 sqrt(3x-1) * d/dx(3x-1)^(1/2)#

#=sec^2 sqrt(3x-1) * 1/2(3x-1)^(-1/2) * d/dx (3x-1)#

#=sec^2 sqrt(3x-1) * 1/ (2 sqrt (3x-1)) * 3#

#=(3 sec^2 sqrt(3x-1) )/ (2 sqrt (3x-1))#

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