derivative f(x)=xsqrt(2x^2+7)

Lösung

ableitung von

f (x) = x 2 x^{2} + 7

\frac{4 x ^{2} + 7}{2 x ^{2} + 7}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

1 \cdot 2 x^{2} + 7 + \frac{2 x}{2 x ^{2} + 7} x : \frac{4 x ^{2} + 7}{2 x ^{2} + 7}

= \frac{4 x ^{2} + 7}{2 x ^{2} + 7}

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

\int sin^{2} (5 θ) d θ

\int \frac{x ^{2} - 5 x + 3}{x - 7} d x

x^{2} + y^{2} = x y y^{^{'}}

in v erse l a pl a ce e^{- 2 s} (\frac{1}{4 s})