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Beliebt Rechnen >

derivative y=x^4cos(4x^2)

Lösung

ableitung von

y = x^{4} cos (4 x^{2})

Lösung

4 x^{3} cos (4 x^{2}) - 8 x^{5} sin (4 x^{2})

Schritte zur Lösung

\frac{d}{d x} (x^{4} cos (4 x^{2}))

Wende die Produktregel an:

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

f = x^{4}, g = cos (4 x^{2})

= \frac{d}{d x} (x^{4}) cos (4 x^{2}) + \frac{d}{d x} (cos (4 x^{2})) x^{4}

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

\frac{d}{d x} (cos (4 x^{2})) = - sin (4 x^{2}) \cdot 8 x

= 4 x^{3} cos (4 x^{2}) + (- sin (4 x^{2}) \cdot 8 x) x^{4}

Vereinfache

4 x^{3} cos (4 x^{2}) + (- sin (4 x^{2}) \cdot 8 x) x^{4} : 4 x^{3} cos (4 x^{2}) - 8 x^{5} sin (4 x^{2})

= 4 x^{3} cos (4 x^{2}) - 8 x^{5} sin (4 x^{2})

Graph

Beliebte Beispiele

fläche y=17x,y=x^2

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\int sin^{2} (t) cos (t) d t

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\int 0.0025 x - 0.075 d x

limit as x approaches 3pi of csc(x)

x \to 3 π lim (csc (x))

y^'-6y=0,y(2)=4

y^{^{'}} - 6 y = 0, y (2) = 4