en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sqrt(1-sec(x))

Solution

derivative of

1 - sec (x)

Solution

- \frac{sec ( x ) tan ( x )}{2 1 - sec ( x )}

Solution steps

\frac{d}{d x} (1 - sec (x))

Apply the chain rule:

\frac{1}{2 1 - sec ( x )} \frac{d}{d x} (1 - sec (x))

= \frac{1}{2 1 - sec ( x )} \frac{d}{d x} (1 - sec (x))

\frac{d}{d x} (1 - sec (x)) = - sec (x) tan (x)

= \frac{1}{2 1 - sec ( x )} (- sec (x) tan (x))

Simplify

\frac{1}{2 1 - sec ( x )} (- sec (x) tan (x)) : - \frac{sec ( x ) tan ( x )}{2 1 - sec ( x )}

= - \frac{sec ( x ) tan ( x )}{2 1 - sec ( x )}

Popular Examples

integral of 6x+4

\int 6 x + 4 d x

integral of (e^{2x})/(e^{2x)+1}

\int \frac{e ^{2 x}}{e ^{2 x} + 1} d x

derivative of (2x^2-13x+20/((x-1)^2))

\frac{d}{d x} (\frac{2 x ^{2} - 13 x + 20}{( x - 1 ) ^{2}})

integral of x^3sqrt(x^2+42)

\int x^{3} x^{2} + 42 d x

limit as x approaches 1 of (x^2+x)/(x-1)

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1-sec(x)) ?
The derivative of sqrt(1-sec(x)) is -(sec(x)tan(x))/(2sqrt(1-sec(x)))
What is the first derivative of sqrt(1-sec(x)) ?
The first derivative of sqrt(1-sec(x)) is -(sec(x)tan(x))/(2sqrt(1-sec(x)))