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Beliebt Rechnen >

derivative f(x)=sqrt(x)sin(x)

Lösung

ableitung von

f (x) = x sin (x)

Lösung

\frac{sin ( x )}{2 x} + x cos (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (x)

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

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

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

= \frac{1}{2 x} sin (x) + cos (x) x

\frac{1}{2 x} sin (x) = \frac{sin ( x )}{2 x}

= \frac{sin ( x )}{2 x} + x cos (x)

Graph

Beliebte Beispiele

y^{''}+1/4 y^'+2y=2cos(4123t)

y^{^{''}} + \frac{1}{4} y^{^{'}} + 2 y = 2 cos (4123 t)

integral of (sqrt(1-4x^2))/x

\int \frac{1 - 4 x ^{2}}{x} d x

derivative of (2x^2+2x+6/(sqrt(x)))

\frac{d}{d x} (\frac{2 x ^{2} + 2 x + 6}{x})

derivative 2/(3t^2)

d er i v a t i v e \frac{2}{3 t ^{2}}

integral of 1/2 x^4

\int \frac{1}{2} x^{4} d x