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What is the derivative of #tan(5x)^(1/2)#?

Answer 1

Isaiah Allen

#(dy)/(dx)=sqrt5/2(x^(-1/2))sec^2(5x)^(1/2)#

#y=tan(5x)^(1/2)#

#u=(5x)^(1/2)=5^(1/2)x^(1/2)#

#=>(dy)/(du)=5^(1/2)1/2x^(-1/2)=sqrt5/2(x^(-1/2))#

#y=tanu=>(dy)/(du)=sec^2u#

#(dy)/(dx)=(dy)/(du)xx(du)/(dx)#

#:.(dy)/(dx)=sec^2uxxsqrt5/2(x^(-1/2))#

#:.(dy)/(dx)=sqrt5/2(x^(-1/2))sec^2(5x)^(1/2)#

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Answer 2

Ezekiel Alexander

The derivative of ( \tan(5x)^{\frac{1}{2}} ) is ( \frac{5\sec^2(5x)}{2\sqrt{\tan(5x)}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.