What is the derivative of (sin(x)/(cos^3(x))) ?

The derivative of (sin(x)/(cos^3(x))) is sec^2(x)(1+3tan^2(x))

What is the first derivative of (sin(x)/(cos^3(x))) ?

The first derivative of (sin(x)/(cos^3(x))) is sec^2(x)(1+3tan^2(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{sin ( x )}{cos ^{3} ( x )})

sec^{2} (x) (1 + 3 tan^{2} (x))

Solution steps

\frac{d}{d x} (\frac{sin ( x )}{cos ^{3} ( x )})

Simplify

\frac{sin ( x )}{cos ^{3} ( x )} : sec^{3} (x) sin (x)

= \frac{d}{d x} (sec^{3} (x) sin (x))

Apply the Product Rule:

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

f = sec^{3} (x), g = sin (x)

= \frac{d}{d x} (sec^{3} (x)) sin (x) + \frac{d}{d x} (sin (x)) sec^{3} (x)

\frac{d}{d x} (sec^{3} (x)) = 3 sec^{3} (x) tan (x)

\frac{d}{d x} (sin (x)) = cos (x)

= 3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x)

Simplify

3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x) : sec^{2} (x) (1 + 3 tan^{2} (x))

= sec^{2} (x) (1 + 3 tan^{2} (x))

f (x) = \frac{2}{x + 5}, at x = 4

n = 1 \sum \infty \frac{6}{n ^{3}}

\int \frac{4 x ^{2} - 2 x}{x} d x

x \to 1 lim (\frac{x ^{3} - 1}{x - 1})

x \to 4 lim (3 (- 3) + 1)

What is the derivative of (sin(x)/(cos^3(x))) ?
The derivative of (sin(x)/(cos^3(x))) is sec^2(x)(1+3tan^2(x))
What is the first derivative of (sin(x)/(cos^3(x))) ?
The first derivative of (sin(x)/(cos^3(x))) is sec^2(x)(1+3tan^2(x))