(\partial)/(\partial y)(4x^{2y})

Lösung

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

8 x^{2 y} ln (x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

= 4 e^{2 y l n (x)} \cdot 2 ln (x)

Vereinfache

4 e^{2 y l n (x)} \cdot 2 ln (x) : 8 x^{2 y} ln (x)

= 8 x^{2 y} ln (x)

\frac{d ^{2} y}{d x ^{2}} = x

t an g e n t f (x) = \frac{x}{x ^{2} + 1}

\frac{d}{d x} (\frac{cot ( x )}{1 + cot ( x )})

im pl i c i t \frac{d y}{d x}, y - 5 x y^{3} + 8 = 5 sin (y^{3} + 2 x^{2})

\frac{\partial}{\partial x} (x (y + 1))