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Beliebt Rechnen >

derivative of xsqrt(2x-3)

Lösung

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

Lösung

\frac{3 x - 3}{2 x - 3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = 2 x - 3

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

\frac{d x}{d x} = 1

\frac{d}{d x} (2 x - 3) = \frac{1}{2 x - 3}

= 1 \cdot 2 x - 3 + \frac{1}{2 x - 3} x

Vereinfache

1 \cdot 2 x - 3 + \frac{1}{2 x - 3} x : \frac{3 x - 3}{2 x - 3}

= \frac{3 x - 3}{2 x - 3}

Graph

Beliebte Beispiele

derivative y=x^2-8x+5

d er i v a t i v e y = x^{2} - 8 x + 5

limit as x approaches 5 of 1

x \to 5 lim (1)

(\partial)/(\partial x)(ln(4x+3y))

\frac{\partial}{\partial x} (ln (4 x + 3 y))

y^'+2y=4cos(2x)

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

integral of (5x^4+8)/(x^5+8x)

\int \frac{5 x ^{4} + 8}{x ^{5} + 8 x} d x