What is the derivative of sqrt(11+tan^2(x)) ?

The derivative of sqrt(11+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(11+tan^2(x)))

What is the first derivative of sqrt(11+tan^2(x)) ?

The first derivative of sqrt(11+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(11+tan^2(x)))

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derivative of

11 + tan^{2} (x)

\frac{sec ^{2} ( x ) tan ( x )}{11 + tan ^{2} ( x )}

Solution steps

\frac{d}{d x} (11 + tan^{2} (x))

Apply the chain rule:

\frac{1}{2 11 + tan ^{2} ( x )} \frac{d}{d x} (11 + tan^{2} (x))

= \frac{1}{2 11 + tan ^{2} ( x )} \frac{d}{d x} (11 + tan^{2} (x))

\frac{d}{d x} (11 + tan^{2} (x)) = 2 sec^{2} (x) tan (x)

= \frac{1}{2 11 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x)

Simplify

\frac{1}{2 11 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x) : \frac{sec ^{2} ( x ) tan ( x )}{11 + tan ^{2} ( x )}

= \frac{sec ^{2} ( x ) tan ( x )}{11 + tan ^{2} ( x )}

n = 0 \sum \infty p (1 - p)^{n}

e^{- x^{2}} cos (x)

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

\frac{d}{d x} (csc^{4} (x))

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

What is the derivative of sqrt(11+tan^2(x)) ?
The derivative of sqrt(11+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(11+tan^2(x)))
What is the first derivative of sqrt(11+tan^2(x)) ?
The first derivative of sqrt(11+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(11+tan^2(x)))