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

Lösung

ableitung von

f (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 f (x) = x^{\frac{5}{2}} (2 - 5 x^{3})

l a pl a ce t r an s f or m e^{(- 2 x)} (3 x)^{2}

t an g e n t f (x) = - 5 sin (x), at x = \frac{π}{4}

\int (4 x^{2} + 3 x - 7) d x

\frac{d}{d x} (x^{2} y^{3} + x^{3} y^{2})