en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of sec(xtan(x))

Solution

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

Solution

- sec (x) + 2 sec^{3} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec (x), g = tan (x)

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

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

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

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

Simplify

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

= - sec (x) + 2 sec^{3} (x)

Popular Examples

(\partial)/(\partial x)(2yln(x))

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

derivative of 10^{sin(pix})

\frac{d}{d x} (1 0^{s i n (π x)})

integral of x/(sqrt(16-9x^2))

\int \frac{x}{16 - 9 x ^{2}} d x

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

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

derivative of (-x+sqrt(1+x)/(x^2-1))

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

Frequently Asked Questions (FAQ)

What is the derivative of sec(xtan(x)) ?
The derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)
What is the first derivative of sec(xtan(x)) ?
The first derivative of sec(xtan(x)) is -sec(x)+2sec^3(x)