derivative xsqrt(2x^2+7)

Lösung

ableitung von

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}

\frac{\partial}{\partial x} (∣ x ∣ y + 2 x)

\int \frac{1 + x}{x} d x

d er i v a t i v e 5 x^{4} (9 - 7 x)^{7}

\int_{- π}^{π} 1

t an g e n t f (x) = x^{3} - 3 x^{2} - 8 x + 9