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Beliebt Rechnen >

derivative of (sqrt(x)-5/(sqrt(x)+6))

Lösung

\frac{d}{d x} (\frac{x - 5}{x + 6})

Lösung

\frac{11}{2 x ( x + 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 5}{x + 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x - 5 ) ( x + 6 ) - \frac{d}{d x} ( x + 6 ) ( x - 5 )}{( x + 6 ) ^{2}}

\frac{d}{d x} (x - 5) = \frac{1}{2 x}

\frac{d}{d x} (x + 6) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 6 ) - \frac{1}{2 x} ( x - 5 )}{( x + 6 ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( x + 6 ) - \frac{1}{2 x} ( x - 5 )}{( x + 6 ) ^{2}} : \frac{11}{2 x ( x + 6 ) ^{2}}

= \frac{11}{2 x ( x + 6 ) ^{2}}

Graph

Beliebte Beispiele

derivative of bx

\frac{d}{d x} (b x)

y^{^{'}} = t + 3

(\partial)/(\partial x)(((3x+5))/(6y+1))

\frac{\partial}{\partial x} (\frac{( 3 x + 5 )}{6 y + 1})

integral from 0 to 2 of pi(4x^2-x^4)

\int_{0}^{2} π (4 x^{2} - x^{4}) d x

tangent y=cos(x),\at x= pi/4

t an g e n t y = cos (x), at x = \frac{π}{4}