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

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

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

The first derivative of f(x)=x^{cos(x)} is x^{cos(x)}(-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 >

derivative of

f (x) = x^{c o s (x)}

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

f (x) = x x, at x = 18

x \to 2 + lim (\frac{1 - x}{x - 2})

\int_{0}^{2} \frac{1}{4 - x ^{2}} d x

\int \frac{5 x ^{2} + 15 x + 8}{( x + 2 ) ^{2} x} d x

y = e^{- 3 x}

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