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How do you differentiate #f(x)=cot(e^sqrt(x^2-1)) # using the chain rule?

1 Answer

Apr 12, 2018

#d/dx f(x)=-csc^2(e^sqrt(x^2-1))(e^sqrt(x^2-1))(1/2(x^2-1)^-(1/2))(2x)#

Explanation:

#d/dxcot(x)=-csc^2(x)#
#d/dxe^x=e^x#
#d/dxx^n=nx^(n-1)#

#f(x)=cot(e^sqrt(x^2-1))#
#d/dx f(x)=-csc^2(e^sqrt(x^2-1))(e^sqrt(x^2-1))(1/2(x^2-1)^-(1/2))(2x)#

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