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

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

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

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

- sin (x) ln (x) + \frac{cos ( x )}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

= \frac{1}{x ^{c o s (x)}} \frac{d}{d x} (x^{c o s (x)})

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

= \frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Simplify

\frac{1}{x ^{c o s (x)}} x^{c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x}) : - sin (x) ln (x) + \frac{cos ( x )}{x}

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

x y + 1 + e = e^{- x y}, (1, - 1)

\int 6 x y^{2} d y

f (x) = e^{x}, at x = ln (14)

x \to 2 lim (2 x - 4 + 8)

\int (cot (x)) d x

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