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Beliebt Rechnen >

derivative of sin(xln(5x))

Lösung

\frac{d}{d x} (sin (x) ln (5 x))

Lösung

cos (x) ln (5 x) + \frac{sin ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (sin (x) ln (5 x))

Wende die Produktregel an:

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

f = sin (x), g = ln (5 x)

= \frac{d}{d x} (sin (x)) ln (5 x) + \frac{d}{d x} (ln (5 x)) sin (x)

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

\frac{d}{d x} (ln (5 x)) = \frac{1}{x}

= cos (x) ln (5 x) + \frac{1}{x} sin (x)

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

= cos (x) ln (5 x) + \frac{sin ( x )}{x}

Graph

Beliebte Beispiele

derivative e^{19}

d er i v a t i v e e^{19}

(dy)/(dx)=e^4x+7y

\frac{d y}{d x} = e^{4} x + 7 y

integral of xsqrt(3x^2-6)

\int x 3 x^{2} - 6 d x

limit as x approaches 2 of (2x^2-5x+2)/(x^3-2x^2)

x \to 2 lim (\frac{2 x ^{2} - 5 x + 2}{x ^{3} - 2 x ^{2}})

derivative of ax^2e^{-3x}

\frac{d}{d x} (a x^{2} e^{- 3 x})