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Beliebt Rechnen >

(\partial)/(\partial x)(3y^2sin(6x))

Lösung

\frac{\partial}{\partial x} (3 y^{2} sin (6 x))

Lösung

18 y^{2} cos (6 x)

Schritte zur Lösung

\frac{\partial}{\partial x} (3 y^{2} sin (6 x))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 y^{2} \frac{\partial}{\partial x} (sin (6 x))

Wende die Kettenregel an:

cos (6 x) \frac{\partial}{\partial x} (6 x)

= cos (6 x) \frac{\partial}{\partial x} (6 x)

\frac{\partial}{\partial x} (6 x) = 6

= 3 y^{2} cos (6 x) \cdot 6

Vereinfache

= 18 y^{2} cos (6 x)

Beliebte Beispiele

xy^'-3y^'-(x-3)sin(x)+y=0

x y^{^{'}} - 3 y^{^{'}} - (x - 3) sin (x) + y = 0

f^'(x)=12x^2-6x+1,f(1)=5

f^{^{'}} (x) = 12 x^{2} - 6 x + 1, f (1) = 5

derivative of-1/6 x^3-1/2 x^2+x+1+ke^k

\frac{d}{d x} (- \frac{1}{6} x^{3} - \frac{1}{2} x^{2} + x + 1 + k e^{k})

integral of 8sec^4(θ)tan^2(θ)

\int 8 sec^{4} (θ) tan^{2} (θ) d θ

(\partial)/(\partial x)(xy+1/x+8/y)

\frac{\partial}{\partial x} (x y + \frac{1}{x} + \frac{8}{y})