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Beliebt Rechnen >

derivative f(x)=5^{sin(x)}

Lösung

ableitung von

f (x) = 5^{s i n (x)}

Lösung

ln (5) \cdot 5^{s i n (x)} cos (x)

Schritte zur Lösung

\frac{d}{d x} (5^{s i n (x)})

Wende Exponentenregel an:

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

5^{s i n (x)} = e^{s i n (x) l n (5)}

= \frac{d}{d x} (e^{s i n (x) l n (5)})

Wende die Kettenregel an:

e^{s i n (x) l n (5)} \frac{d}{d x} (sin (x) ln (5))

= e^{s i n (x) l n (5)} \frac{d}{d x} (sin (x) ln (5))

\frac{d}{d x} (sin (x) ln (5)) = ln (5) cos (x)

= e^{s i n (x) l n (5)} ln (5) cos (x)

e^{s i n (x) l n (5)} = 5^{s i n (x)}

= ln (5) \cdot 5^{s i n (x)} cos (x)

Graph

Beliebte Beispiele

integral from 1 to e of ln(11x)

\int_{1}^{e} ln (11 x) d x

integral of 5^{x^2}

\int 5^{x^{2}} d x

integral of x/(sqrt(36-x^2))

\int \frac{x}{36 - x ^{2}} d x

integral of (5x^3+5x)/(x-1)

\int \frac{5 x ^{3} + 5 x}{x - 1} d x

y^{^{'}} + y = e^{t} + 11