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Popular >

derivative of 1/(cos^3(x))

Solution

\frac{d}{d x} (\frac{1}{cos ^{3} ( x )})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{cos ^{3} ( x )})

Simplify

\frac{1}{cos ^{3} ( x )} : sec^{3} (x)

= \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)) = 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)

Popular Examples

limit as x approaches infinity+of sec(x)

x \to \infty + lim (sec (x))

laplacetransform t^2*sin(1/2 t)laplace transform

t^{2} \cdot sin (\frac{1}{2} t)

integral of x^2e^{4x+3}

\int x^{2} e^{4 x + 3} d x

integral of ((x+6))/(sqrt(5-4x-x^2))

\int \frac{( x + 6 )}{5 - 4 x - x ^{2}} d x

derivative of sqrt(9-x)derivative of

9 - x

Frequently Asked Questions (FAQ)

What is the derivative of 1/(cos^3(x)) ?
The derivative of 1/(cos^3(x)) is 3sec^3(x)tan(x)
What is the first derivative of 1/(cos^3(x)) ?
The first derivative of 1/(cos^3(x)) is 3sec^3(x)tan(x)