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Beliebt Rechnen >

derivative f(x)=4^{sin(2)(x)+cos(3x)}

Lösung

ableitung von

f (x) = 4^{s i n (2) (x) + c o s (3 x)}

Lösung

ln (2) \cdot 2^{2 (s i n (2) x + c o s (3 x)) + 1} (sin (2) - 3 sin (3 x))

Schritte zur Lösung

\frac{d}{d x} (4^{s i n (2) x + c o s (3 x)})

Wende Exponentenregel an:

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

4^{s i n (2) x + c o s (3 x)} = e^{(s i n (2) x + c o s (3 x)) l n (4)}

= \frac{d}{d x} (e^{(s i n (2) x + c o s (3 x)) l n (4)})

Wende die Kettenregel an:

e^{(s i n (2) x + c o s (3 x)) l n (4)} \frac{d}{d x} ((sin (2) x + cos (3 x)) ln (4))

= e^{(s i n (2) x + c o s (3 x)) l n (4)} \frac{d}{d x} ((sin (2) x + cos (3 x)) ln (4))

\frac{d}{d x} ((sin (2) x + cos (3 x)) ln (4)) = 2 ln (2) (sin (2) - sin (3 x) \cdot 3)

= e^{(s i n (2) x + c o s (3 x)) l n (4)} \cdot 2 ln (2) (sin (2) - sin (3 x) \cdot 3)

Vereinfache

e^{(s i n (2) x + c o s (3 x)) l n (4)} \cdot 2 ln (2) (sin (2) - sin (3 x) \cdot 3) : ln (2) \cdot 2^{2 (s i n (2) x + c o s (3 x)) + 1} (sin (2) - 3 sin (3 x))

= ln (2) \cdot 2^{2 (s i n (2) x + c o s (3 x)) + 1} (sin (2) - 3 sin (3 x))

Graph

Beliebte Beispiele

derivative of (x^2/(x-5))

\frac{d}{d x} (\frac{x ^{2}}{x - 5})

integral of (1-tan(x))/(1+tan(x))

\int \frac{1 - tan ( x )}{1 + tan ( x )} d x

limit as x approaches 0 of ((x^3))/(x^3)

x \to 0 lim (\frac{( x ^{3} )}{x ^{3}})

derivative (f(x))/(x^6)

d er i v a t i v e \frac{f ( x )}{x ^{6}}

derivative f(x)= t/(1+t)

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