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Beliebt Rechnen >

derivative of 5^{cos(x})

Lösung

\frac{d}{d x} (5^{c o s (x)})

Lösung

- ln (5) \cdot 5^{c o s (x)} sin (x)

Schritte zur Lösung

\frac{d}{d x} (5^{c o s (x)})

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

e^{c o s (x) l n (5)} \frac{d}{d x} (cos (x) ln (5))

= e^{c o s (x) l n (5)} \frac{d}{d x} (cos (x) ln (5))

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

= e^{c o s (x) l n (5)} (- ln (5) sin (x))

Vereinfache

e^{c o s (x) l n (5)} (- ln (5) sin (x)) : - ln (5) \cdot 5^{c o s (x)} sin (x)

= - ln (5) \cdot 5^{c o s (x)} sin (x)

Graph

Beliebte Beispiele

derivative of (3x^2-2x^3)

\frac{d}{d x} ((3 x^{2} - 2 x)^{3})

limit as x approaches 8/9 of x^4

x \to \frac{8}{9} lim (x^{4})

f (t) = 5 cos (t)

(dy)/(dx)=8x(6y+5)^{1/2}

\frac{d y}{d x} = 8 x (6 y + 5)^{\frac{1}{2}}

integral of (-38y+25)/(-y(7y-5))

\int \frac{- 38 y + 25}{- y ( 7 y - 5 )} d y