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Beliebt Rechnen >

derivative of x^2{z}(x)

Lösung

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

Lösung

2 x z (x) + \frac{d}{d x} (z (x)) x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

Beliebte Beispiele

limit as x approaches e of x^2*e^{x^2}

x \to e lim (x^{2} \cdot e^{x^{2}})

derivative f(x)=2e^x*(x^2+3x-9)^2

d er i v a t i v e f (x) = 2 e^{x} \cdot (x^{2} + 3 x - 9)^{2}

d/(dθ)((cos(θ))/(sin(θ)))

\frac{d}{d θ} (\frac{cos ( θ )}{sin ( θ )})

derivative 2^{4x}

d er i v a t i v e 2^{4 x}

integral of 2xsqrt(4x^2+1)

\int 2 x 4 x^{2} + 1 d x