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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

(cos (x))^{5 l n (x)}

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

Solution steps

\frac{d}{d x} ((cos (x))^{5 l n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\int_{0}^{1} (e^{x})^{2} d x

\int \frac{1}{cos ^{4} ( x )} d x

ln (2 x), y = 0, y = 2

\int \frac{1}{x ^{2} + 8 x + 41} d x

\int 7 sec^{- 2} (x t a) n^{3} x

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