en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=pi^{3x+1}

Solution

derivative of

y = π^{3 x + 1}

Solution

3 ln (π) π^{3 x + 1}

Solution steps

\frac{d}{d x} (π^{3 x + 1})

Apply exponent rule:

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

π^{3 x + 1} = e^{(3 x + 1) l n (π)}

= \frac{d}{d x} (e^{(3 x + 1) l n (π)})

Apply the chain rule:

e^{(3 x + 1) l n (π)} \frac{d}{d x} ((3 x + 1) ln (π))

= e^{(3 x + 1) l n (π)} \frac{d}{d x} ((3 x + 1) ln (π))

\frac{d}{d x} ((3 x + 1) ln (π)) = 3 ln (π)

= e^{(3 x + 1) l n (π)} \cdot 3 ln (π)

e^{(3 x + 1) l n (π)} = π^{3 x + 1}

= 3 ln (π) π^{3 x + 1}

Popular Examples

\frac{d z}{d z}

derivative of (x+y+1^2)

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

derivative of f(x)=cos(a^9+x^9)derivative of

f (x) = cos (a^{9} + x^{9})

integral of x/(sqrt(25-4x^2))

\int \frac{x}{25 - 4 x ^{2}} d x

integral from-infinity to 0 of 3^x

\int_{- \infty}^{0} 3^{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=pi^{3x+1} ?
The derivative of y=pi^{3x+1} is 3ln(pi)pi^{3x+1}
What is the first derivative of y=pi^{3x+1} ?
The first derivative of y=pi^{3x+1} is 3ln(pi)pi^{3x+1}