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Popular >

derivative of xsec(xtan(x))

Solution

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

Solution

sec (x) tan (x) + x (- sec (x) + 2 sec^{3} (x))

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sec (x) tan (x)

= \frac{d x}{d x} sec (x) tan (x) + \frac{d}{d x} (sec (x) tan (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sec (x) tan (x)) = - sec (x) + 2 sec^{3} (x)

= 1 \cdot sec (x) tan (x) + (- sec (x) + 2 sec^{3} (x)) x

Simplify

= sec (x) tan (x) + x (- sec (x) + 2 sec^{3} (x))

Graph

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3

Frequently Asked Questions (FAQ)

What is the derivative of xsec(xtan(x)) ?
The derivative of xsec(xtan(x)) is sec(x)tan(x)+x(-sec(x)+2sec^3(x))
What is the first derivative of xsec(xtan(x)) ?
The first derivative of xsec(xtan(x)) is sec(x)tan(x)+x(-sec(x)+2sec^3(x))