derivative of x^2sqrt(4x-3)

Lösung

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

\frac{10 x ^{2} - 6 x}{4 x - 3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = 4 x - 3

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

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

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

= 2 x 4 x - 3 + \frac{2}{4 x - 3} x^{2}

Vereinfache

2 x 4 x - 3 + \frac{2}{4 x - 3} x^{2} : \frac{10 x ^{2} - 6 x}{4 x - 3}

= \frac{10 x ^{2} - 6 x}{4 x - 3}

x \to 4 - lim (x^{2} + 2)

x \to 0 - lim (\frac{2}{9 x ^{\frac{1}{3}}})

y^{^{'}} = (x + y - 4) 2

a re a y = 3 x, y = \frac{1}{x}

d er i v a t i v e f (x) = 2 - 6 x