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How do you differentiate #f(x)=tan(5x^3)#?

Answer 1

Ezekiel Alexander

#d/dx tan(5x^3)=15x^2sec^2(5x^3)##

In order to differentiate this function, we need to use the chain rule for #tan(f(x))#:

#d/dxtan(f(x))=sec^2(f(x))xxf'(x)#

#d/dx tan(5x^3)=sec^2(5x^3)15x^2=15x^2sec^2(5x^3)#

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Answer 2

Charles Arocha

To differentiate ( f(x) = \tan(5x^3) ), you would use the chain rule. The derivative is ( f'(x) = 15x^2 \sec^2(5x^3) ).

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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.

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