de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of 2^xx^2

Lösung

\frac{d}{d x} (2^{x} x^{2})

Lösung

ln (2) \cdot 2^{x} x^{2} + 2^{1 + x} x

Schritte zur Lösung

\frac{d}{d x} (2^{x} x^{2})

Wende die Produktregel an:

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

f = 2^{x}, g = x^{2}

= \frac{d}{d x} (2^{x}) x^{2} + \frac{d}{d x} (x^{2}) 2^{x}

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

\frac{d}{d x} (x^{2}) = 2 x

= 2^{x} ln (2) x^{2} + 2 x \cdot 2^{x}

Wende Exponentenregel an:

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

2 \cdot 2^{x} = 2^{1 + x}

= ln (2) \cdot 2^{x} x^{2} + 2^{1 + x} x

Graph

Beliebte Beispiele

integral of 1/(8-7x)

\int \frac{1}{8 - 7 x} d x

integral of (x^2+2x)cos(x)

\int (x^{2} + 2 x) cos (x) d x

derivative of sqrt((x^4))

\frac{d}{d x} ((x^{4}))

y^{''}+4y=5sin(2x)

y^{^{''}} + 4 y = 5 sin (2 x)

integral from 7 to infinity of xe^{-4x}

\int_{7}^{\infty} x e^{- 4 x} d x