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

The derivative of sqrt(tan^2(x)+1) is tan(x)sqrt(sec^2(x))

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

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

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derivative of

tan^{2} (x) + 1

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y e^{x}

y^{^{'}} = y (5 - y)

\int x^{- 2} e^{x} d x

\int_{0}^{7} \frac{1}{x x} d x

\int + e^{2 x - 1} d x

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