derivative sqrt((4+x^2)/(4-x))

Lösung

ableitung von

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

\frac{- x ^{2} + 8 x + 4}{2 x ^{2} + 4 ( - x + 4 ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 \frac{4 + x ^{2}}{4 - x}} \cdot \frac{- x ^{2} + 8 x + 4}{( 4 - x ) ^{2}} : \frac{- x ^{2} + 8 x + 4}{2 x ^{2} + 4 ( - x + 4 ) ^{\frac{3}{2}}}

= \frac{- x ^{2} + 8 x + 4}{2 x ^{2} + 4 ( - x + 4 ) ^{\frac{3}{2}}}

t an g e n t f (x) = (12 x - 8)^{\frac{1}{2}}, at x = 2

\frac{d y}{d x} = 7 x y^{2}

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

\int_{1}^{2} x e^{x} d x

d er i v a t i v e f (x) = 5^{s i n (x)}