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Beliebt Rechnen >

derivative of 4^{cos(x})

Lösung

\frac{d}{d x} (4^{c o s (x)})

Lösung

- ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

Schritte zur Lösung

\frac{d}{d x} (4^{c o s (x)})

Wende Exponentenregel an:

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

4^{c o s (x)} = e^{c o s (x) l n (4)}

= \frac{d}{d x} (e^{c o s (x) l n (4)})

Wende die Kettenregel an:

e^{c o s (x) l n (4)} \frac{d}{d x} (cos (x) ln (4))

= e^{c o s (x) l n (4)} \frac{d}{d x} (cos (x) ln (4))

\frac{d}{d x} (cos (x) ln (4)) = - 2 ln (2) sin (x)

= e^{c o s (x) l n (4)} (- 2 ln (2) sin (x))

Vereinfache

e^{c o s (x) l n (4)} (- 2 ln (2) sin (x)) : - ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

= - ln (2) \cdot 2^{2 c o s (x) + 1} sin (x)

Graph

Beliebte Beispiele

integral of (x^3)/((x^2+1)^2)

\int \frac{x ^{3}}{( x ^{2} + 1 ) ^{2}} d x

limit as x approaches-5 of (x-5)/(x+5)

x \to - 5 lim (\frac{x - 5}{x + 5})

a re a x^{2}, 9

xy^'+y=50sqrt(x)

x y^{^{'}} + y = 50 x

derivative f(x)=(8x)/(e^x)

d er i v a t i v e f (x) = \frac{8 x}{e ^{x}}