derivative of ((7x^2-8^4)/x)

Lösung

\frac{d}{d x} (\frac{( 7 x ^{2} - 8 ) ^{4}}{x})

\frac{56 x ^{2} ( 7 x ^{2} - 8 ) ^{3} - ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 7 x ^{2} - 8 ) ^{4}}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( 7 x ^{2} - 8 ) ^{4} ) x - \frac{d x}{d x} ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

\frac{d}{d x} ((7 x^{2} - 8)^{4}) = 56 x (7 x^{2} - 8)^{3}

\frac{d x}{d x} = 1

= \frac{56 x ( 7 x ^{2} - 8 ) ^{3} x - 1 \cdot ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}

56 x (7 x^{2} - 8)^{3} x - 1 \cdot (7 x^{2} - 8)^{4} = 56 x^{2} (7 x^{2} - 8)^{3} - (7 x^{2} - 8)^{4}

= \frac{56 x ^{2} ( 7 x ^{2} - 8 ) ^{3} - ( 7 x ^{2} - 8 ) ^{4}}{x ^{2}}