derivative of ((x^2-4^3)/(x^2+2))

Lösung

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

\frac{6 x ( x ^{2} - 4 ) ^{2} ( x ^{2} + 2 ) - 2 x ( x ^{2} - 4 ) ^{3}}{( x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} ((x^{2} - 4)^{3}) = 6 x (x^{2} - 4)^{2}

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

= \frac{6 x ( x ^{2} - 4 ) ^{2} ( x ^{2} + 2 ) - 2 x ( x ^{2} - 4 ) ^{3}}{( x ^{2} + 2 ) ^{2}}

f (X) = ln (ln (ln (tan (X))))

\frac{\partial}{\partial x} (y \cdot ln (x) + \frac{1}{9} y^{3})

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

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

\int \frac{e ^{2 x}}{9 + e ^{4 x}} d x