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What is the Derivative of #y=sec(x^2)#?

Answer 1

Ezra Adams

#y'=2x*sec(x^2)tan(x^2)#

Solution

let's #y=f(g(x))#

Using Chain Rule, we get

#y'=f'(g(x))*g'(x)#

for given problem, which is

#y=sec(x^2)#

differentiating with respect to #x# using Chain Rule,

#y'=sec(x^2)tan(x^2)*(x^2)'#

#y'=sec(x^2)tan(x^2)*2x#

#y'=2x*sec(x^2)tan(x^2)#

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Answer 2

William Abdalla

The derivative of ( y = \sec(x^2) ) is ( \frac{d}{dx}(\sec(x^2)) = 2x \sec(x^2) \tan(x^2) ).

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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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