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

The derivative of x^{xcos(x}) is x^{xcos(x)}(cos(x)ln(x)-xsin(x)ln(x)+cos(x))

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

x^{2} + 4 ln^{2} (x)

ln (x^{2})

\frac{- 3 x ^{5} - x ^{4} - x ^{3} + 4 x ^{2}}{x ^{2}}

x \frac{d y}{d x} = 4 y

y = x^{3}, x = - 1, x = 2, y = 0

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