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Beliebt Rechnen >

(\partial)/(\partial x)(2x*sin(9x^2y))

Lösung

\frac{\partial}{\partial x} (2 x \cdot sin (9 x^{2} y))

Lösung

2 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x sin (9 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (x sin (9 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (9 x^{2} y)

= 2 (\frac{\partial}{\partial x} (x) sin (9 x^{2} y) + \frac{\partial}{\partial x} (sin (9 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (9 x^{2} y)) = cos (9 x^{2} y) \cdot 18 y x

= 2 (1 \cdot sin (9 x^{2} y) + cos (9 x^{2} y) \cdot 18 y xx)

Vereinfache

2 (1 \cdot sin (9 x^{2} y) + cos (9 x^{2} y) \cdot 18 y xx) : 2 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))

= 2 (sin (9 x^{2} y) + 18 x^{2} y cos (9 x^{2} y))

Beliebte Beispiele

integral of 1/(sqrt(25x^2+1))

\int \frac{1}{25 x ^{2} + 1} d x

sum from n=1 to infinity of 3/(4+6n)

n = 1 \sum \infty \frac{3}{4 + 6 n}

sum from n=1 to infinity of 2/(3n+5)

n = 1 \sum \infty \frac{2}{3 n + 5}

sin (x) d x + y d y = 0

integral of x^9e^{x^5}

\int x^{9} e^{x^{5}} d x