What is the derivative of 5^{sin(pix}) ?

The derivative of 5^{sin(pix}) is piln(5)*5^{sin(pix)}cos(pix)

What is the first derivative of 5^{sin(pix}) ?

The first derivative of 5^{sin(pix}) is piln(5)*5^{sin(pix)}cos(pix)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (5^{s i n (π x)})

π ln (5) \cdot 5^{s i n (π x)} cos (π x)

Solution steps

\frac{d}{d x} (5^{s i n (π x)})

Apply exponent rule:

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

5^{s i n (π x)} = e^{s i n (π x) l n (5)}

= \frac{d}{d x} (e^{s i n (π x) l n (5)})

Apply the chain rule:

e^{s i n (π x) l n (5)} \frac{d}{d x} (sin (π x) ln (5))

= e^{s i n (π x) l n (5)} \frac{d}{d x} (sin (π x) ln (5))

\frac{d}{d x} (sin (π x) ln (5)) = ln (5) cos (π x) π

= e^{s i n (π x) l n (5)} ln (5) cos (π x) π

e^{s i n (π x) l n (5)} = 5^{s i n (π x)}

= π ln (5) \cdot 5^{s i n (π x)} cos (π x)

\frac{e ^{x}}{1}

\frac{d}{d u} (4 u)

\int \frac{3 x - 3}{x ^{2} - x - 2} d x

\int 0.5 e^{- 0.5 (x - 1)} d x

\frac{d}{d x} (\frac{1}{x ^{4} + x ^{2} + 1})

What is the derivative of 5^{sin(pix}) ?
The derivative of 5^{sin(pix}) is piln(5)*5^{sin(pix)}cos(pix)
What is the first derivative of 5^{sin(pix}) ?
The first derivative of 5^{sin(pix}) is piln(5)*5^{sin(pix)}cos(pix)