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Beliebt Rechnen >

(\partial)/(\partial x)(5sin(2x)cos(5y))

Lösung

\frac{\partial}{\partial x} (5 sin (2 x) cos (5 y))

Lösung

10 cos (2 x) cos (5 y)

Schritte zur Lösung

\frac{\partial}{\partial x} (5 sin (2 x) cos (5 y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 5 cos (5 y) \frac{\partial}{\partial x} (sin (2 x))

Wende die Kettenregel an:

cos (2 x) \frac{\partial}{\partial x} (2 x)

= cos (2 x) \frac{\partial}{\partial x} (2 x)

\frac{\partial}{\partial x} (2 x) = 2

= 5 cos (5 y) cos (2 x) \cdot 2

Vereinfache

= 10 cos (2 x) cos (5 y)

Beliebte Beispiele

integral from 0 to 3 of sqrt(3x+16)

\int_{0}^{3} 3 x + 16 d x

derivative y=ln|sin(x)|

d er i v a t i v e y = ln ∣ sin (x) ∣

derivative of (x^{2-x}^5(x-3x^2))

\frac{d}{d x} ((x^{2 - x})^{5} (x - 3 x^{2}))

integral of (81)/(x^3-9x^2)

\int \frac{81}{x ^{3} - 9 x ^{2}} d x

tangent (x^2+1)/(x^2+x+1)

t an g e n t \frac{x ^{2} + 1}{x ^{2} + x + 1}