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Beliebt Rechnen >

derivative of (x^2+x+1/x)

Lösung

\frac{d}{d x} (\frac{x ^{2} + x + 1}{x})

Lösung

\frac{x ^{2} - 1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + x + 1}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x^{2} + x + 1) = 2 x + 1

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

= \frac{( 2 x + 1 ) x - 1 \cdot ( x ^{2} + x + 1 )}{x ^{2}}

Vereinfache

\frac{( 2 x + 1 ) x - 1 \cdot ( x ^{2} + x + 1 )}{x ^{2}} : \frac{x ^{2} - 1}{x ^{2}}

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

Graph

Beliebte Beispiele

y^{^{''}} + 9 y = 0

tangent y=10cot((pix)/(20)),\at x=5

t an g e n t y = 10 cot (\frac{π x}{20}), at x = 5

derivative of (3+x{f}(x)/(sqrt(x)))

\frac{d}{d x} (\frac{3 + x f ( x )}{x})

derivative (arctan(4x))^2

d er i v a t i v e (arctan (4 x))^{2}

2(d^2y)/(dx^2)+8y=cos(2x)

2 \frac{d ^{2} y}{d x ^{2}} + 8 y = cos (2 x)