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How do you find the derivative of #y=tan^ntheta#?

Answer 1

William Abdalla

#(dy)/(d theta)=ntan^(n-1) thetasec^2 theta#

we need the chain rule

#(dy)/(d theta)=(dy)/(du)(du)/(d theta)#

#y=tan^n theta#

#u=tan theta=>(du)/(d theta)=sec^2 theta#

#:.y=u^n=>(dy)/(du)=n u^(n-1)#

#(dy)/(dx)=n u^(n-1)xxsec^2 theta#

#(dy)/(dx)=ntan^(n-1) thetasec^2 theta#

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Answer 2

Isaiah Allen

To find the derivative of ( y = \tan^n(\theta) ), where ( n ) is a constant, you can use the chain rule. The derivative is ( \frac{dy}{d\theta} = n \tan^{n-1}(\theta) \sec^2(\theta) ).

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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.