derivative y=x^2sqrt(2x-7)

Lösung

ableitung von

y = x^{2} 2 x - 7

\frac{5 x ^{2} - 14 x}{2 x - 7}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 2 x - 7)

Wende die Produktregel an:

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

f = x^{2}, g = 2 x - 7

= \frac{d}{d x} (x^{2}) 2 x - 7 + \frac{d}{d x} (2 x - 7) x^{2}

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

\frac{d}{d x} (2 x - 7) = \frac{1}{2 x - 7}

= 2 x 2 x - 7 + \frac{1}{2 x - 7} x^{2}

Vereinfache

2 x 2 x - 7 + \frac{1}{2 x - 7} x^{2} : \frac{5 x ^{2} - 14 x}{2 x - 7}

= \frac{5 x ^{2} - 14 x}{2 x - 7}

\int (2 x^{2} + 1) e^{(x^{2})} d x

x \frac{d y}{d x} = \frac{1}{y ^{3}}

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