What is the derivative of y=sqrt(10+tan^2(x)) ?

The derivative of y=sqrt(10+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(10+tan^2(x)))

What is the first derivative of y=sqrt(10+tan^2(x)) ?

The first derivative of y=sqrt(10+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(10+tan^2(x)))

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derivative of

y = 10 + tan^{2} (x)

\frac{sec ^{2} ( x ) tan ( x )}{10 + tan ^{2} ( x )}

Solution steps

\frac{d}{d x} (10 + tan^{2} (x))

Apply the chain rule:

\frac{1}{2 10 + tan ^{2} ( x )} \frac{d}{d x} (10 + tan^{2} (x))

= \frac{1}{2 10 + tan ^{2} ( x )} \frac{d}{d x} (10 + tan^{2} (x))

\frac{d}{d x} (10 + tan^{2} (x)) = 2 sec^{2} (x) tan (x)

= \frac{1}{2 10 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x)

Simplify

\frac{1}{2 10 + tan ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x) : \frac{sec ^{2} ( x ) tan ( x )}{10 + tan ^{2} ( x )}

= \frac{sec ^{2} ( x ) tan ( x )}{10 + tan ^{2} ( x )}

\int \frac{cot ( β )}{sin ^{6} ( β )} d β

\int \frac{1}{1 + \frac{1}{x}} d x

\frac{d}{d x} (4 x + 2)

\frac{d}{d x} (\frac{8}{3 + x ^{2}})

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

What is the derivative of y=sqrt(10+tan^2(x)) ?
The derivative of y=sqrt(10+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(10+tan^2(x)))
What is the first derivative of y=sqrt(10+tan^2(x)) ?
The first derivative of y=sqrt(10+tan^2(x)) is (sec^2(x)tan(x))/(sqrt(10+tan^2(x)))