What is the derivative of sec^3(sqrt(x)) ?

The derivative of sec^3(sqrt(x)) is (3sec^3(sqrt(x))tan(sqrt(x)))/(2sqrt(x))

What is the first derivative of sec^3(sqrt(x)) ?

The first derivative of sec^3(sqrt(x)) is (3sec^3(sqrt(x))tan(sqrt(x)))/(2sqrt(x))

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\frac{d}{d x} (sec^{3} (x))

\frac{3 sec ^{3} ( x ) tan ( x )}{2 x}

Solution steps

\frac{d}{d x} (sec^{3} (x))

Apply the chain rule:

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

= 3 (sec (x))^{2} \frac{d}{d x} (sec (x))

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

= 3 (sec (x))^{2} \frac{sec ( x ) tan ( x )}{2 x}

Simplify

3 sec^{2} (x) \frac{sec ( x ) tan ( x )}{2 x} : \frac{3 sec ^{3} ( x ) tan ( x )}{2 x}

= \frac{3 sec ^{3} ( x ) tan ( x )}{2 x}

What is the derivative of sec^3(sqrt(x)) ?
The derivative of sec^3(sqrt(x)) is (3sec^3(sqrt(x))tan(sqrt(x)))/(2sqrt(x))
What is the first derivative of sec^3(sqrt(x)) ?
The first derivative of sec^3(sqrt(x)) is (3sec^3(sqrt(x))tan(sqrt(x)))/(2sqrt(x))