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Beliebt Rechnen >

(\partial)/(\partial x)(2xsin(8x^2y))

Lösung

\frac{\partial}{\partial x} (2 x sin (8 x^{2} y))

Lösung

2 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x sin (8 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (x sin (8 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (8 x^{2} y)

= 2 (\frac{\partial}{\partial x} (x) sin (8 x^{2} y) + \frac{\partial}{\partial x} (sin (8 x^{2} y)) x)

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

\frac{\partial}{\partial x} (sin (8 x^{2} y)) = cos (8 x^{2} y) \cdot 16 y x

= 2 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx)

Vereinfache

2 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx) : 2 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

= 2 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

Beliebte Beispiele

y^'=0.0012y(1700-y)

y^{^{'}} = 0.0012 y (1700 - y)

y^'=((2x^2+3y^2))/(2xy)

y^{^{'}} = \frac{( 2 x ^{2} + 3 y ^{2} )}{2 x y}

(\partial)/(\partial v)(tan(u/v))

\frac{\partial}{\partial v} (tan (\frac{u}{v}))

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

n = 3 \sum \infty \frac{2}{n ( n + 2 )}

integral of-5csc^2(x)

\int - 5 csc^{2} (x) d x