What is (\partial)/(\partial x)(tan(sqrt(x))) ?

The answer to (\partial)/(\partial x)(tan(sqrt(x))) is (sec^2(sqrt(x)))/(2sqrt(x))

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(\partial)/(\partial x)(tan(sqrt(x)))

\frac{\partial}{\partial x} (tan (x))

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

Solution steps

\frac{\partial}{\partial x} (tan (x))

Apply the chain rule:

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

= sec^{2} (x) \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (x) = \frac{1}{2 x}

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

Simplify

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

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

\frac{d ^{4}}{d x ^{4}} (3 e^{x^{2}})

4 y^{^{''}} - 4 y^{^{'}} + y = 0

n = 1 \sum \infty ln (\frac{1}{n ^{2}})

\frac{d}{d x} (2 x (3 x^{2} - 7)^{3})

x \to 3 lim (\frac{x ^{2} - 1}{x - 3})

What is (\partial)/(\partial x)(tan(sqrt(x))) ?
The answer to (\partial)/(\partial x)(tan(sqrt(x))) is (sec^2(sqrt(x)))/(2sqrt(x))