derivative of (sqrt(x)+1/(sqrt(x)+4))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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

x \to 3 + lim (\frac{x + 3}{x - 3})

\frac{\partial}{\partial x} (\frac{x}{x ^{6} - y ^{7}})

n = 4 \sum \infty (x + 1)^{n}

d er i v a t i v e f (x) = x^{- 8}