What is the derivative of x^{-5cos(x}) ?

The derivative of x^{-5cos(x}) is x^{-5cos(x)}(5sin(x)ln(x)-(5cos(x))/x)

What is the first derivative of x^{-5cos(x}) ?

The first derivative of x^{-5cos(x}) is x^{-5cos(x)}(5sin(x)ln(x)-(5cos(x))/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} (x^{- 5 c o s (x)})

x^{- 5 c o s (x)} (5 sin (x) ln (x) - \frac{5 cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{- 5 c o s (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{- 5 c o s (x)} = e^{(- 5 c o s (x)) l n (x)}

= \frac{d}{d x} (e^{(- 5 c o s (x)) l n (x)})

Apply the chain rule:

e^{(- 5 c o s (x)) l n (x)} \frac{d}{d x} ((- 5 cos (x)) ln (x))

= e^{(- 5 c o s (x)) l n (x)} \frac{d}{d x} ((- 5 cos (x)) ln (x))

\frac{d}{d x} ((- 5 cos (x)) ln (x)) = 5 sin (x) ln (x) - \frac{5 cos ( x )}{x}

= e^{(- 5 c o s (x)) l n (x)} (5 sin (x) ln (x) - \frac{5 cos ( x )}{x})

Simplify

e^{(- 5 c o s (x)) l n (x)} (5 sin (x) ln (x) - \frac{5 cos ( x )}{x}) : x^{- 5 c o s (x)} (5 sin (x) ln (x) - \frac{5 cos ( x )}{x})

= x^{- 5 c o s (x)} (5 sin (x) ln (x) - \frac{5 cos ( x )}{x})

x \to 1 lim (4 x^{2} + 2 x + 5)

\frac{d}{d x} (- 3 ln (x))

\int t sin (\frac{t}{2}) d t

\int \frac{x + 5}{x ^{2} + 4} d x

\int_{0}^{1} \frac{1}{x ^{2} - 1} d x

What is the derivative of x^{-5cos(x}) ?
The derivative of x^{-5cos(x}) is x^{-5cos(x)}(5sin(x)ln(x)-(5cos(x))/x)
What is the first derivative of x^{-5cos(x}) ?
The first derivative of x^{-5cos(x}) is x^{-5cos(x)}(5sin(x)ln(x)-(5cos(x))/x)