derivative of (sqrt(x-3)/(sqrt(x+3)))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{x - 3}{x + 3} : \frac{x - 3}{x + 3}

= \frac{d}{d x} (\frac{x - 3}{x + 3})

Wende die Kettenregel an:

\frac{1}{2 \frac{x - 3}{x + 3}} \frac{d}{d x} (\frac{x - 3}{x + 3})

= \frac{1}{2 \frac{x - 3}{x + 3}} \frac{d}{d x} (\frac{x - 3}{x + 3})

\frac{d}{d x} (\frac{x - 3}{x + 3}) = \frac{6}{( x + 3 ) ^{2}}

= \frac{1}{2 \frac{x - 3}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{x - 3}{x + 3}} \cdot \frac{6}{( x + 3 ) ^{2}} : \frac{3}{x - 3 ( x + 3 ) ^{\frac{3}{2}}}

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

d er i v a t i v e x^{2} + 7

\int x^{2} 2 x - 1 d x

\frac{d x}{d t} + t^{7} x^{9} + \frac{x}{t} = 0

\frac{d ^{2}}{d x ^{2}} (cos (sin (3 θ)))

t an g e n t f (x) = - \frac{24}{( 4 x + 1 )}, at x = - 1