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)(4x^{-x^2-y^2-z^2})

Lösung

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

Lösung

4 x^{- x^{2} - y^{2} - z^{2}} (- 2 x ln (x) + \frac{- x ^{2} - y ^{2} - z ^{2}}{x})

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{- x^{2} - y^{2} - z^{2}} = e^{(- x^{2} - y^{2} - z^{2}) l n (x)}

= 4 \frac{\partial}{\partial x} (e^{(- x^{2} - y^{2} - z^{2}) l n (x)})

Wende die Kettenregel an:

e^{(- x^{2} - y^{2} - z^{2}) l n (x)} \frac{\partial}{\partial x} ((- x^{2} - y^{2} - z^{2}) ln (x))

= e^{(- x^{2} - y^{2} - z^{2}) l n (x)} \frac{\partial}{\partial x} ((- x^{2} - y^{2} - z^{2}) ln (x))

\frac{\partial}{\partial x} ((- x^{2} - y^{2} - z^{2}) ln (x)) = - 2 x ln (x) + \frac{- x ^{2} - y ^{2} - z ^{2}}{x}

= 4 e^{(- x^{2} - y^{2} - z^{2}) l n (x)} (- 2 x ln (x) + \frac{- x ^{2} - y ^{2} - z ^{2}}{x})

e^{(- x^{2} - y^{2} - z^{2}) l n (x)} = x^{- x^{2} - y^{2} - z^{2}}

= 4 x^{- x^{2} - y^{2} - z^{2}} (- 2 x ln (x) + \frac{- x ^{2} - y ^{2} - z ^{2}}{x})

Beliebte Beispiele

integral of 7.9t-16.6

\int 7.9 t - 16.6 d t

derivative of 1/((1-2x^{3/2)})

\frac{d}{d x} (\frac{1}{( 1 - 2 x ) ^{\frac{3}{2}}})

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

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

integral of 1/(sqrt(64+x^2))

\int \frac{1}{64 + x ^{2}} d x

f (x) = x cos (x)