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How do you differentiate #f(x)=tan(3x-x^2) # using the chain rule?

Answer 1

Ezekiel Alexander

#f'(x)=(3-2x)sec^2(3x-x^2)#

#"given "f(x)=g(h(x))" then"#

#f'(x)=g'(h(x))xxh'(x)larr" chain rule"#

#rArrf'(x)=sec^2(3x-x^2)xxd/dx(3x-x^2)#

#color(white)(rArrf'(x))=(3-2x)sec^2(3x-x^2)#

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Answer 2

Scarlett Allison

To differentiate ( f(x) = \tan(3x - x^2) ) using the chain rule, first, identify the outer function and the inner function. In this case, the outer function is ( \tan(x) ) and the inner function is ( 3x - x^2 ).

The derivative of ( \tan(x) ) is ( \sec^2(x) ). The derivative of the inner function, ( 3x - x^2 ), with respect to ( x ) is ( 3 - 2x ).

Now, applying the chain rule, the derivative of ( f(x) ) is given by: [ f'(x) = \sec^2(3x - x^2) \cdot (3 - 2x) ]

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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.