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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{5 x ^{2} - 6 x}{2 x - 3}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x 2 x - 3 + \frac{1}{2 x - 3} x^{2} : \frac{5 x ^{2} - 6 x}{2 x - 3}

= \frac{5 x ^{2} - 6 x}{2 x - 3}

Graph

Beliebte Beispiele

x^2y^'+4/3 xy=-4cos(3x)y^{-1/2}

x^{2} y^{^{'}} + \frac{4}{3} x y = - 4 cos (3 x) y^{- \frac{1}{2}}

limit as x approaches 1+of 1/(x^2-1)

x \to 1 + lim (\frac{1}{x ^{2} - 1})

y^{''}-4y=0,y(0)=0,y^'(0)=1

y^{^{''}} - 4 y = 0, y (0) = 0, y^{^{'}} (0) = 1

tangent f(x)= 4/(1+x^2),(1,2)

t an g e n t f (x) = \frac{4}{1 + x ^{2}}, (1, 2)

inverselaplace (3s+4)/(s^2+2)

in v erse l a pl a ce \frac{3 s + 4}{s ^{2} + 2}