What is the derivative of (tan(x)/(cos(x))) ?

The derivative of (tan(x)/(cos(x))) is -sec(x)+2sec^3(x)

What is the first derivative of (tan(x)/(cos(x))) ?

The first derivative of (tan(x)/(cos(x))) is -sec(x)+2sec^3(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Simplify

\frac{tan ( x )}{cos ( x )} : sec (x) tan (x)

= \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)

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