derivative of ((x^2+1)/((x+4)))

Lösung

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{( x + 4 )})

\frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} + 1 )}{( x + 4 )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 1 ) ( x + 4 ) - \frac{d}{d x} ( x + 4 ) ( x ^{2} + 1 )}{( x + 4 ) ^{2}}

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

\frac{d}{d x} (x + 4) = 1

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

Vereinfache

\frac{2 x ( x + 4 ) - 1 \cdot ( x ^{2} + 1 )}{( x + 4 ) ^{2}} : \frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

= \frac{x ^{2} + 8 x - 1}{( x + 4 ) ^{2}}

d er i v a t i v e y = (5 x + 1)^{3} (x - 4)

\int \frac{x}{( x ^{2} - 4 )} d x

d er i v a t i v e sin (8 x)

\int_{0}^{5} \frac{1}{x ^{\frac{13}{14}}} d x

y^{^{''}} + 2 y^{^{'}} - 2 y = 0