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

Lösung

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

8 y^{4 x} ln (y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

y^{4 x} = e^{4 x l n (y)}

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (4 x ln (y)) = 4 ln (y)

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

Vereinfache

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

= 8 y^{4 x} ln (y)

t an g e n t f (x) = sin (x) + 1, at x = - \frac{π}{2}

a re a f (x) = x^{2} - 4, x = - 4, x = 3

\int \frac{1}{x ^{2} a ^{2} - x ^{2}} d x

x \to - 3 lim (∣ x ∣ - 2)

l a pl a ce t r an s f or m e^{t}