What is the derivative of 2^{sin(pix}) ?

The derivative of 2^{sin(pix}) is piln(2)*2^{sin(pix)}cos(pix)

What is the first derivative of 2^{sin(pix}) ?

The first derivative of 2^{sin(pix}) is piln(2)*2^{sin(pix)}cos(pix)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (2^{s i n (π x)})

π ln (2) \cdot 2^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (2^{s i n (π x)})

Apply exponent rule:

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

2^{s i n (π x)} = e^{s i n (π x) l n (2)}

= \frac{d}{d x} (e^{s i n (π x) l n (2)})

Apply the chain rule:

e^{s i n (π x) l n (2)} \frac{d}{d x} (sin (π x) ln (2))

= e^{s i n (π x) l n (2)} \frac{d}{d x} (sin (π x) ln (2))

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

= e^{s i n (π x) l n (2)} ln (2) cos (π x) π

e^{s i n (π x) l n (2)} = 2^{s i n (π x)}

= π ln (2) \cdot 2^{s i n (π x)} cos (π x)

What is the derivative of 2^{sin(pix}) ?
The derivative of 2^{sin(pix}) is piln(2)*2^{sin(pix)}cos(pix)
What is the first derivative of 2^{sin(pix}) ?
The first derivative of 2^{sin(pix}) is piln(2)*2^{sin(pix)}cos(pix)