de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial x)(-5xcos(x^2-5xy))

Lösung

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

Lösung

- 5 (cos (x^{2} - 5 x y) - x sin (x^{2} - 5 x y) (2 x - 5 y))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x^{2} - 5 x y)

= - 5 (\frac{\partial}{\partial x} (x) cos (x^{2} - 5 x y) + \frac{\partial}{\partial x} (cos (x^{2} - 5 x y)) x)

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

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

= - 5 (1 \cdot cos (x^{2} - 5 x y) + (- sin (x^{2} - 5 x y) (2 x - 5 y)) x)

Vereinfache

= - 5 (cos (x^{2} - 5 x y) - x sin (x^{2} - 5 x y) (2 x - 5 y))

Beliebte Beispiele

(d^2)/(dx)(y)+2(dy)/(dx)+y=0

\frac{d ^{2}}{d x} (y) + 2 \frac{d y}{d x} + y = 0

(\partial)/(\partial x)(e^{-2z}ysin(x))

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

fläche cos(θ),0.5

a re a cos (θ), 0.5

derivative 153x^2-0.06x^3

d er i v a t i v e 153 x^{2} - 0.06 x^{3}

derivative y=(3/5 x)^4

d er i v a t i v e y = (\frac{3}{5} x)^{4}