What is the derivative of 2^{cos(x}) ?

The derivative of 2^{cos(x}) is -ln(2)*2^{cos(x)}sin(x)

What is the first derivative of 2^{cos(x}) ?

The first derivative of 2^{cos(x}) is -ln(2)*2^{cos(x)}sin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (2^{c o s (x)})

- ln (2) \cdot 2^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (2^{c o s (x)})

Apply exponent rule:

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

2^{c o s (x)} = e^{c o s (x) l n (2)}

= \frac{d}{d x} (e^{c o s (x) l n (2)})

Apply the chain rule:

e^{c o s (x) l n (2)} \frac{d}{d x} (cos (x) ln (2))

= e^{c o s (x) l n (2)} \frac{d}{d x} (cos (x) ln (2))

\frac{d}{d x} (cos (x) ln (2)) = - ln (2) sin (x)

= e^{c o s (x) l n (2)} (- ln (2) sin (x))

Simplify

e^{c o s (x) l n (2)} (- ln (2) sin (x)) : - ln (2) \cdot 2^{c o s (x)} sin (x)

= - ln (2) \cdot 2^{c o s (x)} sin (x)

What is the derivative of 2^{cos(x}) ?
The derivative of 2^{cos(x}) is -ln(2)*2^{cos(x)}sin(x)
What is the first derivative of 2^{cos(x}) ?
The first derivative of 2^{cos(x}) is -ln(2)*2^{cos(x)}sin(x)