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Popular >

derivative of xsec(x)

Solution

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

Solution

sec (x) + x sec (x) tan (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = sec (x)

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

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

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

= 1 \cdot sec (x) + sec (x) tan (x) x

Simplify

= sec (x) + x sec (x) tan (x)

Popular Examples

integral of (cos(θ))

\int (cos (θ)) d θ

tangent of x^3-3x+4 tangent of

x^{3} - 3 x + 4

integral of (x^3)/(x^2+1)

\int \frac{x ^{3}}{x ^{2} + 1} d x

(\partial)/(\partial x)(x^1y^2+y^4z^5)

\frac{\partial}{\partial x} (x^{1} y^{2} + y^{4} z^{5})

integral of sin^2(2x)cos^3(2x)

\int sin^{2} (2 x) cos^{3} (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of xsec(x) ?
The derivative of xsec(x) is sec(x)+xsec(x)tan(x)
What is the first derivative of xsec(x) ?
The first derivative of xsec(x) is sec(x)+xsec(x)tan(x)