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Beliebt Rechnen >

derivative f(x)=(1+2e^x)sin(x)

Lösung

ableitung von

f (x) = (1 + 2 e^{x}) sin (x)

Lösung

2 e^{x} sin (x) + cos (x) (1 + 2 e^{x})

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 1 + 2 e^{x}, g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= 2 e^{x} sin (x) + cos (x) (1 + 2 e^{x})

Graph

Beliebte Beispiele

d er i v a t i v e - 2^{x}

derivative 1/4*x^2-((sin(2x^2)))/8

d er i v a t i v e \frac{1}{4} \cdot x^{2} - \frac{( sin ( 2 x ^{2} ) )}{8}

derivative sin^4(3x-4x^2)

d er i v a t i v e sin^{4} (3 x - 4 x^{2})

derivative-(e^{-x})^2

d er i v a t i v e - (e^{- x})^{2}

derivative log_{10}(x-1)

d er i v a t i v e lo g_{10} (x - 1)