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Beliebt Rechnen >

(\partial)/(\partial x)(6xsin(x+2y-z))

Lösung

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

Lösung

6 (sin (x + 2 y - z) + x cos (x + 2 y - z))

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial x} (x sin (x + 2 y - z))

Wende die Produktregel an:

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

f = x, g = sin (x + 2 y - z)

= 6 (\frac{\partial}{\partial x} (x) sin (x + 2 y - z) + \frac{\partial}{\partial x} (sin (x + 2 y - z)) x)

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

\frac{\partial}{\partial x} (sin (x + 2 y - z)) = cos (x + 2 y - z)

= 6 (1 \cdot sin (x + 2 y - z) + cos (x + 2 y - z) x)

Vereinfache

= 6 (sin (x + 2 y - z) + x cos (x + 2 y - z))

Beliebte Beispiele

(\partial)/(\partial y)(2x^2+2y-8)

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

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

\int (csc^{2} (x) + 4) d x

derivative of x^2*e^{2x}

\frac{d}{d x} (x^{2} \cdot e^{2 x})

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

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

xy^2y^'=y^3-5x^3,y(1)=2

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 2