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Beliebt Rechnen >

derivative of xsin(9x)

Lösung

\frac{d}{d x} (x sin (9 x))

Lösung

sin (9 x) + 9 x cos (9 x)

Schritte zur Lösung

\frac{d}{d x} (x sin (9 x))

Wende die Produktregel an:

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

f = x, g = sin (9 x)

= \frac{d x}{d x} sin (9 x) + \frac{d}{d x} (sin (9 x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sin (9 x)) = cos (9 x) \cdot 9

= 1 \cdot sin (9 x) + cos (9 x) \cdot 9 x

Vereinfache

= sin (9 x) + 9 x cos (9 x)

Graph

Beliebte Beispiele

integral of 5/(sqrt(x)(1+5\sqrt{x))^2}

\int \frac{5}{x ( 1 + 5 x ) ^{2}} d x

integral of (e^{3x})/(4+e^{3x)}

\int \frac{e ^{3 x}}{4 + e ^{3 x}} d x

(d^3)/(dx^3)(x(2x-5)^3)

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

integral of 5/244 x^4

\int \frac{5}{244} x^{4} d x

integral of cos^2(x)sin(x)

\int cos^{2} (x) sin (x) d x