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Beliebt Rechnen >

derivative f(x)=e^xsin^2(x)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

integral from 0 to t of te^{-t}

\int_{0}^{t} t e^{- t} d t

(\partial)/(\partial x)(e^{x-2})

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

derivative of 8x^3+4x^2-5x+4

\frac{d}{d x} (8 x^{3} + 4 x^{2} - 5 x + 4)

derivative arcsin(5x)

d er i v a t i v e arcsin (5 x)

derivative ((8x)^9)/9

d er i v a t i v e \frac{( 8 x ) ^{9}}{9}