What is the derivative of sec^2(sqrt(x)) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{sin ( x )}{8 x e ^{x}})

\frac{d}{d t} (t^{5})

x \to 0 lim (tan (x) ln (x))

\frac{1}{x ^{5}}

\int (x + 1) (2 x^{2} + x) d x

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