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Popular >

derivative of sqrt(1+tan^2(x))

Solution

\frac{d}{d x} (1 + tan^{2} (x))

Solution

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

Solution steps

\frac{d}{d x} (1 + tan^{2} (x))

Apply the chain rule:

\frac{1}{2 1 + tan ^{2} ( x )} \frac{d}{d x} (1 + tan^{2} (x))

= \frac{1}{2 1 + tan ^{2} ( x )} \frac{d}{d x} (1 + tan^{2} (x))

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

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

Simplify

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

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

Popular Examples

derivative of 1/((x^2+y^2))

\frac{d}{d x} (\frac{1}{( x ^{2} + y ^{2} )})

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

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

integral of sin^3(x)-sin^5(x)

\int sin^{3} (x) - sin^{5} (x) d x

derivative of f(x)= x/(x^2-4)derivative of

f (x) = \frac{x}{x ^{2} - 4}

9x^2y^'=y^'+6xe^{-y}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1+tan^2(x)) ?
The derivative of sqrt(1+tan^2(x)) is tan(x)sqrt(sec^2(x))
What is the first derivative of sqrt(1+tan^2(x)) ?
The first derivative of sqrt(1+tan^2(x)) is tan(x)sqrt(sec^2(x))