What is the derivative of y=(cos(3x))^x ?

The derivative of y=(cos(3x))^x is cos^x(3x)(ln(cos(3x))-3xtan(3x))

What is the first derivative of y=(cos(3x))^x ?

The first derivative of y=(cos(3x))^x is cos^x(3x)(ln(cos(3x))-3xtan(3x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = (cos (3 x))^{x}

cos^{x} (3 x) (ln (cos (3 x)) - 3 x tan (3 x))

Solution steps

\frac{d}{d x} ((cos (3 x))^{x})

Apply exponent rule:

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

(cos (3 x))^{x} = e^{x l n (c o s (3 x))}

= \frac{d}{d x} (e^{x l n (c o s (3 x))})

Apply the chain rule:

e^{x l n (c o s (3 x))} \frac{d}{d x} (x ln (cos (3 x)))

= e^{x l n (c o s (3 x))} \frac{d}{d x} (x ln (cos (3 x)))

\frac{d}{d x} (x ln (cos (3 x))) = ln (cos (3 x)) - 3 x tan (3 x)

= e^{x l n (c o s (3 x))} (ln (cos (3 x)) - 3 x tan (3 x))

e^{x l n (c o s (3 x))} = cos^{x} (3 x)

= cos^{x} (3 x) (ln (cos (3 x)) - 3 x tan (3 x))

x \to 0 lim (\frac{sin ( 4 x )}{x})

\frac{d}{d x} (A cos (2 x))

\int sin (nπ x) d x

\frac{d}{d x} ((x + 1) (x + 3))

\frac{( x + 1 )}{( 5 - x )}

What is the derivative of y=(cos(3x))^x ?
The derivative of y=(cos(3x))^x is cos^x(3x)(ln(cos(3x))-3xtan(3x))
What is the first derivative of y=(cos(3x))^x ?
The first derivative of y=(cos(3x))^x is cos^x(3x)(ln(cos(3x))-3xtan(3x))