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Beliebt Rechnen >

derivative of {f}(x(e^x))

Lösung

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

Lösung

\frac{d}{d x} (f (x)) e^{x} + e^{x} f (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = f (x), g = e^{x}

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

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

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

Beliebte Beispiele

sum from n=0 to infinity of 3(-1/3)^n

n = 0 \sum \infty 3 (- \frac{1}{3})^{n}

tangent y=x^3-2x+1,(4,57)

t an g e n t y = x^{3} - 2 x + 1, (4, 57)

y^{^{'}} = \frac{x}{6 y}

(dy)/(dt)=0.12-(6y)/(50-2t)

\frac{d y}{d t} = 0.12 - \frac{6 y}{50 - 2 t}

integral of 3tan^2(x)

\int 3 tan^{2} (x) d x