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Popular >

derivative of |sec(x|)

Solution

\frac{d}{d x} (∣ sec (x) ∣)

Solution

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

Solution steps

\frac{d}{d x} (∣ sec (x) ∣)

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial y)(ln(x^2-y^2))

\frac{\partial}{\partial y} (ln (x^{2} - y^{2}))

derivative of (1+x^2)^2 derivative of

(1 + x^{2})^{2}

integral of (7x^5+6x^4-3x^3-9x+5)

\int (7 x^{5} + 6 x^{4} - 3 x^{3} - 9 x + 5) d x

integral of (x^2-64)/(x(x-1)^2)

\int \frac{x ^{2} - 64}{x ( x - 1 ) ^{2}} d x

integral of 1/(ysqrt(1+(ln(y))^2))

\int \frac{1}{y 1 + ( ln ( y ) ) ^{2}} d y

Frequently Asked Questions (FAQ)

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