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)(3x*e^{2x+y^2})

Lösung

\frac{\partial}{\partial x} (3 x \cdot e^{2 x + y^{2}})

Lösung

3 (e^{2 x + y^{2}} + 2 e^{2 x + y^{2}} x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x e^{2 x + y^{2}})

Wende die Produktregel an:

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

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

= 3 (\frac{\partial}{\partial x} (x) e^{2 x + y^{2}} + \frac{\partial}{\partial x} (e^{2 x + y^{2}}) x)

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

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

= 3 (1 \cdot e^{2 x + y^{2}} + e^{2 x + y^{2}} \cdot 2 x)

Vereinfache

= 3 (e^{2 x + y^{2}} + 2 e^{2 x + y^{2}} x)

Beliebte Beispiele

derivative of xsqrt(3-2x^2)

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

integral of u/(sqrt(u^2-1))

\int \frac{u}{u ^{2} - 1} d u

(dN)/(dt)=(te^t)/(N^2)

\frac{d N}{d t} = \frac{t e ^{t}}{N ^{2}}

sum from n=0 to infinity of 1/(n^5)

n = 0 \sum \infty \frac{1}{n ^{5}}

sum from n=8 to infinity of (1/4)^n

n = 8 \sum \infty (\frac{1}{4})^{n}