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Beliebt Rechnen >

derivative of xsqrt(x^2+4)

Lösung

\frac{d}{d x} (x x^{2} + 4)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (x x^{2} + 4)

Wende die Produktregel an:

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

f = x, g = x^{2} + 4

= \frac{d x}{d x} x^{2} + 4 + \frac{d}{d x} (x^{2} + 4) x

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

\frac{d}{d x} (x^{2} + 4) = \frac{x}{x ^{2} + 4}

= 1 \cdot x^{2} + 4 + \frac{x}{x ^{2} + 4} x

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (2x+2)

\int (2 x + 2) d x

(\partial)/(\partial x)(x^2+y^2+x+y+xy)

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

derivative f(x)=(2x^3+4x+1)

d er i v a t i v e f (x) = (2 x^{3} + 4 x + 1)

integral of (4+4tan^2(v))

\int (4 + 4 tan^{2} (v)) d v

(sin (\frac{x}{2}))^{^{'}}