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)(4(x-y)e^{4y+4x^2})

Lösung

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

Lösung

4 (e^{4 y + 4 x^{2}} + 8 e^{4 y + 4 x^{2}} x (x - y))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x - y, g = e^{4 y + 4 x^{2}}

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

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

\frac{\partial}{\partial x} (e^{4 y + 4 x^{2}}) = e^{4 y + 4 x^{2}} \cdot 8 x

= 4 (1 \cdot e^{4 y + 4 x^{2}} + e^{4 y + 4 x^{2}} \cdot 8 x (x - y))

Vereinfache

= 4 (e^{4 y + 4 x^{2}} + 8 e^{4 y + 4 x^{2}} x (x - y))

Beliebte Beispiele

x^{''}+3x^'-10x=6e^{4t}

x^{^{''}} + 3 x^{^{'}} - 10 x = 6 e^{4 t}

(\partial)/(\partial x)(2yx^2-4)

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

derivative sqrt(r^2-13x^2)

d er i v a t i v e r^{2} - 13 x^{2}

y^'=3-2x-0.5y,y(0)=1

y^{^{'}} = 3 - 2 x - 0.5 y, y (0) = 1

derivative of (ln(x)^{sec(x)})

\frac{d}{d x} ((ln (x))^{s e c (x)})