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Beliebt Rechnen >

(\partial)/(\partial x)(x*sin(x)-1)

Lösung

\frac{\partial}{\partial x} (x \cdot sin (x) - 1)

Lösung

x cos (x) + sin (x)

Schritte zur Lösung

\frac{\partial}{\partial x} (x sin (x) - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x sin (x)) - \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (1) = 0

= sin (x) + x cos (x) - 0

Vereinfache

= x cos (x) + sin (x)

Beliebte Beispiele

sum from n=1 to infinity of ne^{-n/2}

n = 1 \sum \infty n e^{- \frac{n}{2}}

integral of (4x+2)/(x^2)

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

derivative of arccot(e^x)

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

integral of (3x^2)/(x^2-1)

\int \frac{3 x ^{2}}{x ^{2} - 1} d x

limit as x approaches 5+of (2x)/(x-5)

x \to 5 + lim (\frac{2 x}{x - 5})