derivative of x^2y-4x^3+34^2

Lösung

\frac{d}{d x} (x^{2} \cdot y - 4 x^{3} + 3 \cdot 4^{2})

x^{2} \frac{d y}{d x} - 12 x^{2} + 2 x y

Schritte zur Lösung

\frac{d}{d x} (x^{2} y - 4 x^{3} + 3 \cdot 4^{2})

Vereinfache

x^{2} y - 4 x^{3} + 3 \cdot 4^{2} : x^{2} y - 4 x^{3} + 48

= \frac{d}{d x} (x^{2} y - 4 x^{3} + 48)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2} y) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (48)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (48) = 0

= 2 x y + \frac{d y}{d x} x^{2} - 12 x^{2} + 0

Vereinfache

= x^{2} \frac{d y}{d x} - 12 x^{2} + 2 x y

d er i v a t i v e ln ((2 x - 3)^{2})

d er i v a t i v e (\frac{1}{x}) (x^{2} - 2)

d er i v a t i v e sin (x^{\frac{1}{3}})

d er i v a t i v e 5 (4 x - 3)^{- 1}

d er i v a t i v e \frac{1}{( 2 + x ^{2} )}