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Beliebt Rechnen >

derivative 7^{x^4+x}

Lösung

ableitung von

7^{x^{4} + x}

Lösung

ln (7) \cdot 7^{x^{4} + x} (4 x^{3} + 1)

Schritte zur Lösung

\frac{d}{d x} (7^{x^{4} + x})

Wende Exponentenregel an:

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

7^{x^{4} + x} = e^{(x^{4} + x) l n (7)}

= \frac{d}{d x} (e^{(x^{4} + x) l n (7)})

Wende die Kettenregel an:

e^{(x^{4} + x) l n (7)} \frac{d}{d x} ((x^{4} + x) ln (7))

= e^{(x^{4} + x) l n (7)} \frac{d}{d x} ((x^{4} + x) ln (7))

\frac{d}{d x} ((x^{4} + x) ln (7)) = ln (7) (4 x^{3} + 1)

= e^{(x^{4} + x) l n (7)} ln (7) (4 x^{3} + 1)

e^{(x^{4} + x) l n (7)} = 7^{x^{4} + x}

= ln (7) \cdot 7^{x^{4} + x} (4 x^{3} + 1)

Graph

Beliebte Beispiele

tangent y=3x-2sqrt(x),(1,1)

t an g e n t y = 3 x - 2 x, (1, 1)

(2e^y-x)(dy)/(dx)=1

(2 e^{y} - x) \frac{d y}{d x} = 1

derivative of (7+x^5)

\frac{d}{d x} ((7 + x)^{5})

limit as x approaches-0 of ln(x)

x \to - 0 lim (ln (x))

derivative y=(x^2+32sqrt(x))/8 ,x=4

d er i v a t i v e y = \frac{x ^{2} + 32 x}{8}, x = 4