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Beliebt Rechnen >

derivative of a(e^{bx}+be^{bx}x)

Lösung

\frac{d}{d x} (a (e^{b x} + b e^{b x} x))

Lösung

a (b^{2} e^{b x} x + 2 b e^{b x})

Schritte zur Lösung

\frac{d}{d x} (a (e^{b x} + b e^{b x} x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (e^{b x} + b e^{b x} x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= a (\frac{d}{d x} (e^{b x}) + \frac{d}{d x} (b e^{b x} x))

\frac{d}{d x} (e^{b x}) = e^{b x} b

\frac{d}{d x} (b e^{b x} x) = b (b e^{b x} x + e^{b x})

= a (e^{b x} b + b (b e^{b x} x + e^{b x}))

Multipliziere aus

e^{b x} b + b (b e^{b x} x + e^{b x}) : b^{2} e^{b x} x + 2 b e^{b x}

= a (b^{2} e^{b x} x + 2 b e^{b x})

Graph

Beliebte Beispiele

(\partial)/(\partial x)(xsqrt((4-x^2)))

\frac{\partial}{\partial x} (x (4 - x^{2}))

y^{''}-4y^'+4y=x^2e^x

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{2} e^{x}

y^'-y/x =xcos(x)

y^{^{'}} - \frac{y}{x} = x cos (x)

derivative of 1/4 x^4-2x^2

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

d x + e^{8 x} d y = 0