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Beliebt Rechnen >

(\partial)/(\partial x)(5sin(3x)cos(4y))

Lösung

\frac{\partial}{\partial x} (5 sin (3 x) cos (4 y))

Lösung

15 cos (3 x) cos (4 y)

Schritte zur Lösung

\frac{\partial}{\partial x} (5 sin (3 x) cos (4 y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 cos (4 y) \frac{\partial}{\partial x} (sin (3 x))

Wende die Kettenregel an:

cos (3 x) \frac{\partial}{\partial x} (3 x)

= cos (3 x) \frac{\partial}{\partial x} (3 x)

\frac{\partial}{\partial x} (3 x) = 3

= 5 cos (4 y) cos (3 x) \cdot 3

Vereinfache

= 15 cos (3 x) cos (4 y)

Beliebte Beispiele

y^'=-2y+5t,y(0)=-4

y^{^{'}} = - 2 y + 5 t, y (0) = - 4

(\partial)/(\partial z)(2x^{y/z})

\frac{\partial}{\partial z} (2 x^{\frac{y}{z}})

tangent y=4sqrt(x)

t an g e n t y = 4 x

(\partial)/(\partial x)(x^3y^2-4yx^2+3yx-4)

\frac{\partial}{\partial x} (x^{3} y^{2} - 4 y x^{2} + 3 y x - 4)

tangent y=x^2+5x+6,\at x=7

t an g e n t y = x^{2} + 5 x + 6, at x = 7