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Beliebt Rechnen >

derivative f(x)=x^4cos(x)

Lösung

ableitung von

f (x) = x^{4} cos (x)

Lösung

4 x^{3} cos (x) - x^{4} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{4} cos (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = cos (x)

= \frac{d}{d x} (x^{4}) cos (x) + \frac{d}{d x} (cos (x)) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} cos (x) + (- sin (x)) x^{4}

Vereinfache

= 4 x^{3} cos (x) - x^{4} sin (x)

Graph

Beliebte Beispiele

integral of e^{-2x}

\int e^{- 2 x} d x

\frac{d y}{d t} + y = t

(df)/(dx)=4x^2-5x+log_{10}(x)

\frac{df}{d x} = 4 x^{2} - 5 x + lo g_{10} (x)

integral of (2x)/(x-1)

\int \frac{2 x}{x - 1} d x

limit as x approaches 0+of 9

x \to 0 + lim (9)