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Popular >

derivative of xsec^2(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = sec^{2} (x)

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

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

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

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

Simplify

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

Popular Examples

y^'=(x^3+y^3)/(xy^2)

y^{^{'}} = \frac{x ^{3} + y ^{3}}{x y ^{2}}

\frac{d y}{d x} y = 11 x

tangent of f(x)=-x^4+4x^3+8x^2+5,\at x=2 tangent of

f (x) = - x^{4} + 4 x^{3} + 8 x^{2} + 5, at x = 2

d/(dt)(t^2+3t-2)

\frac{d}{d t} (t^{2} + 3 t - 2)

(\partial)/(\partial x)(7e^{8x})

\frac{\partial}{\partial x} (7 e^{8 x})

Frequently Asked Questions (FAQ)

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