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Beliebt Rechnen >

derivative of (x^2+sqrt(x)3^x)

Lösung

\frac{d}{d x} ((x^{2} + x) 3^{x})

Lösung

(2 x + \frac{1}{2 x}) \cdot 3^{x} + 3^{x} ln (3) (x^{2} + x)

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + x) \cdot 3^{x})

Wende die Produktregel an:

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

f = x^{2} + x, g = 3^{x}

= \frac{d}{d x} (x^{2} + x) 3^{x} + \frac{d}{d x} (3^{x}) (x^{2} + x)

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

\frac{d}{d x} (3^{x}) = 3^{x} ln (3)

= (2 x + \frac{1}{2 x}) \cdot 3^{x} + 3^{x} ln (3) (x^{2} + x)

Graph

Beliebte Beispiele

integral from-8 to 18 of 1/(sqrt(|2x|))

\int_{- 8}^{18} \frac{1}{∣ 2 x ∣} d x

(\partial)/(\partial y)(3y^2+x^2-3)

\frac{\partial}{\partial y} (3 y^{2} + x^{2} - 3)

(d^3)/(dx^3)(e^x)

\frac{d ^{3}}{d x ^{3}} (e^{x})

integral of cos^4(5x+5)

\int cos^{4} (5 x + 5) d x

integral of log_{2}(x-4)

\int lo g_{2} (x - 4) d x