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Popular Calculus >

derivative of f(x)=tan(sec(cos(x)))

Solution

derivative of

f (x) = tan (sec (cos (x)))

Solution

- sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)

Solution steps

\frac{d}{d x} (tan (sec (cos (x))))

Apply the chain rule:

sec^{2} (sec (cos (x))) \frac{d}{d x} (sec (cos (x)))

= sec^{2} (sec (cos (x))) \frac{d}{d x} (sec (cos (x)))

\frac{d}{d x} (sec (cos (x))) = - sec (cos (x)) tan (cos (x)) sin (x)

= sec^{2} (sec (cos (x))) (- sec (cos (x)) tan (cos (x)) sin (x))

Simplify

= - sec^{2} (sec (cos (x))) sec (cos (x)) tan (cos (x)) sin (x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=tan(sec(cos(x))) ?
The derivative of f(x)=tan(sec(cos(x))) is -sec^2(sec(cos(x)))sec(cos(x))tan(cos(x))sin(x)
What is the first derivative of f(x)=tan(sec(cos(x))) ?
The first derivative of f(x)=tan(sec(cos(x))) is -sec^2(sec(cos(x)))sec(cos(x))tan(cos(x))sin(x)