CALCULUS DIFFERENTATION QUESTION

Question

find derivative of tan(secx)

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Answer 1

We have two functions here, an outer function which is tan and an inner function which is sec. We have to use the chain rule, which says we take the derivative of the outer function and multiply it by the derivative of the inner function.

The derivative of the outer function, tan(x), is sec²(x) but here we will replace (x) with (sec x) so we get sec²(sec x)

The derivative of the inner function, sec (x), is tan(x)sec(x)

So for our final answer we multiply these two derivatives together and we get

sec²(sec (x))tan(x)sec(x)

Answer 2

We can find this derivative using chain rule.

The derivative of tan(x) is sec²(x)

The derivative of sec(x) is sec(x) tan(x)

Hence the derivative of tan(sec(x))

d(tan(sec(x))/dx = sec²(sec(x)) sec(x) tan(x)