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

The derivative of (sec(x)^3) is 3sec^3(x)tan(x)

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

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

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

3 sec^{3} (x) tan (x)

Solution steps

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

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)) = sec (x) tan (x)

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

Simplify

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

= 3 sec^{3} (x) tan (x)

\frac{d}{d x} (d cos (t) + t^{2} sin (t))

\frac{d x}{d t} = x^{2} + \frac{1}{25}

d er i v a t i v e f (x) = (x - 1) e^{x}

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

\int \frac{9 - x ^{2}}{x ^{2}} d x

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