What is the derivative of f(x)=x^pi*pi^x ?

The derivative of f(x)=x^pi*pi^x is pi^{1+x}x^{pi-1}+ln(pi)pi^xx^pi

What is the first derivative of f(x)=x^pi*pi^x ?

The first derivative of f(x)=x^pi*pi^x is pi^{1+x}x^{pi-1}+ln(pi)pi^xx^pi

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = x^{π} \cdot π^{x}

π^{1 + x} x^{π - 1} + ln (π) π^{x} x^{π}

Solution steps

\frac{d}{d x} (x^{π} π^{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{π}, g = π^{x}

= \frac{d}{d x} (x^{π}) π^{x} + \frac{d}{d x} (π^{x}) x^{π}

\frac{d}{d x} (x^{π}) = π x^{π - 1}

\frac{d}{d x} (π^{x}) = π^{x} ln (π)

= π x^{π - 1} π^{x} + π^{x} ln (π) x^{π}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

π π^{x} = π^{1 + x}

= π^{1 + x} x^{π - 1} + ln (π) π^{x} x^{π}

\int 12 x^{2} sin (6 - x^{3}) d x

\int \frac{x}{2 x ^{2} - x + 1} d x

\int_{- 1}^{1} \frac{1}{x + 1} d x

\frac{d y}{d t} - 2 t y = 15 t^{2} e^{t^{2}}

\int x^{3} + x d x

What is the derivative of f(x)=x^pi*pi^x ?
The derivative of f(x)=x^pi*pi^x is pi^{1+x}x^{pi-1}+ln(pi)pi^xx^pi
What is the first derivative of f(x)=x^pi*pi^x ?
The first derivative of f(x)=x^pi*pi^x is pi^{1+x}x^{pi-1}+ln(pi)pi^xx^pi