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Beliebt Rechnen >

derivative of 4x^{2x}

Lösung

\frac{d}{d x} (4 x^{2 x})

Lösung

8 x^{2 x} (ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (4 x^{2 x})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2 x})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x ln (x)) = 2 (ln (x) + 1)

= 4 e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

Vereinfache

4 e^{2 x l n (x)} \cdot 2 (ln (x) + 1) : 8 x^{2 x} (ln (x) + 1)

= 8 x^{2 x} (ln (x) + 1)

Graph

Beliebte Beispiele

integral from 1 to 2 of (x^2+1)

\int_{1}^{2} (x^{2} + 1) d x

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

\int \frac{2 x}{( 1 + x ) ^{2}} d x

integral of 3/(t^2)

\int \frac{3}{t ^{2}} d t

(\partial)/(\partial x)(sec^5(x^3y^3))

\frac{\partial}{\partial x} (sec^{5} (x^{3} y^{3}))

derivative f(x)=x+1+1/(x^2)

d er i v a t i v e f (x) = x + 1 + \frac{1}{x ^{2}}