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Beliebt Rechnen >

derivative f(x)=x^2cos(x)

Lösung

ableitung von

f (x) = x^{2} cos (x)

Lösung

2 x cos (x) - x^{2} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{2} cos (x))

Wende die Produktregel an:

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

f = x^{2}, g = cos (x)

= \frac{d}{d x} (x^{2}) cos (x) + \frac{d}{d x} (cos (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x cos (x) + (- sin (x)) x^{2}

Vereinfache

= 2 x cos (x) - x^{2} sin (x)

Graph

Beliebte Beispiele

derivative of sqrt(sin(3x))

\frac{d}{d x} (sin (3 x))

f^'(x)=-(4x)/((1+2x^2)^2)

f^{^{'}} (x) = - \frac{4 x}{( 1 + 2 x ^{2} ) ^{2}}

(6y+2x-7)dx+(4y+6x-1)dy=0

(6 y + 2 x - 7) d x + (4 y + 6 x - 1) d y = 0

integral from-1 to 1 of 2-|x|

\int_{- 1}^{1} 2 - ∣ x ∣ d x

integral of 1/(e^{-t)}

\int \frac{1}{e ^{- t}} d t