What is the derivative of (cos(4x)^x) ?

The derivative of (cos(4x)^x) is cos^x(4x)(ln(cos(4x))-4xtan(4x))

What is the first derivative of (cos(4x)^x) ?

The first derivative of (cos(4x)^x) is cos^x(4x)(ln(cos(4x))-4xtan(4x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

cos^{x} (4 x) (ln (cos (4 x)) - 4 x tan (4 x))

Solution steps

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

Apply exponent rule:

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

(cos (4 x))^{x} = e^{x l n (c o s (4 x))}

= \frac{d}{d x} (e^{x l n (c o s (4 x))})

Apply the chain rule:

e^{x l n (c o s (4 x))} \frac{d}{d x} (x ln (cos (4 x)))

= e^{x l n (c o s (4 x))} \frac{d}{d x} (x ln (cos (4 x)))

\frac{d}{d x} (x ln (cos (4 x))) = ln (cos (4 x)) - 4 x tan (4 x)

= e^{x l n (c o s (4 x))} (ln (cos (4 x)) - 4 x tan (4 x))

e^{x l n (c o s (4 x))} = cos^{x} (4 x)

= cos^{x} (4 x) (ln (cos (4 x)) - 4 x tan (4 x))

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

(\frac{x + 2}{x - 2})^{5}

f (1) = 2 x^{3}

\frac{1}{s ^{3} ( s + 1 )}

\int 0.06 x - 0.6 - \frac{7700}{x ^{2}} d x

What is the derivative of (cos(4x)^x) ?
The derivative of (cos(4x)^x) is cos^x(4x)(ln(cos(4x))-4xtan(4x))
What is the first derivative of (cos(4x)^x) ?
The first derivative of (cos(4x)^x) is cos^x(4x)(ln(cos(4x))-4xtan(4x))