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Popular Calculus >

derivative of sec^5(x)

Solution

derivative of

sec^{5} (x)

Solution

5 sec^{5} (x) tan (x)

Solution steps

\frac{d}{d x} (sec^{5} (x))

Apply the chain rule:

5 (sec (x))^{4} \frac{d}{d x} (sec (x))

= 5 (sec (x))^{4} \frac{d}{d x} (sec (x))

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

= 5 (sec (x))^{4} sec (x) tan (x)

Simplify

5 sec^{4} (x) sec (x) tan (x) : 5 sec^{5} (x) tan (x)

= 5 sec^{5} (x) tan (x)

Graph

Popular Examples

integral from 1200 to 1210 of x*0.1

\int_{1200}^{1210} x \cdot 0.1 d x

derivative of ((4x^3+5)/(-5x^2+1))^{1/4}

d er i v a t i v e (\frac{4 x ^{3} + 5}{- 5 x ^{2} + 1})^{\frac{1}{4}}

derivative of (x^2)/(5(4-x))

d er i v a t i v e \frac{x ^{2}}{5 ( 4 - x )}

integral from-3 to 0 of 1/(sqrt(1-x))

\int_{- 3}^{0} \frac{1}{1 - x} d x

integral of-x^2y^2sin(x)+2xy^2cos(x)

\int - x^{2} y^{2} sin (x) + 2 x y^{2} cos (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of sec^5(x) ?
The derivative of sec^5(x) is 5sec^5(x)tan(x)
What is the first derivative of sec^5(x) ?
The first derivative of sec^5(x) is 5sec^5(x)tan(x)