What is the derivative of tan(sqrt(x)) ?

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

What is the first derivative of tan(sqrt(x)) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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 y}{d x} = - \frac{y ln ( y )}{x}

y^{^{'}} = x y - sin (x) e^{- x^{2}} y^{3}

\frac{d}{d x} (\frac{ln ( 3 )}{x})

y^{^{''}} + 6 y^{^{'}} + 4 y = 0

\int_{0}^{\frac{π}{2}} 9 cos^{2} (x) d x

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