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

Lösung

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

\frac{- 2 - 9 x}{( 3 x - 2 ) ^{5}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((3 x - 2)^{4}) = 12 (3 x - 2)^{3}

= \frac{1 \cdot ( 3 x - 2 ) ^{4} - 12 ( 3 x - 2 ) ^{3} x}{( ( 3 x - 2 ) ^{4} ) ^{2}}

Vereinfache

\frac{1 \cdot ( 3 x - 2 ) ^{4} - 12 ( 3 x - 2 ) ^{3} x}{( ( 3 x - 2 ) ^{4} ) ^{2}} : \frac{- 2 - 9 x}{( 3 x - 2 ) ^{5}}

= \frac{- 2 - 9 x}{( 3 x - 2 ) ^{5}}

\int (sec^{2} (x) + 7) d x

t an g e n t f (x) = - 3 x^{4}, at x = - 1

\int_{- 2}^{3} (x^{2} + 4) - (- x^{2} - 1) d x

x \to \infty lim (8^{- x})

d er i v a t i v e p (x) = 2 x^{4} + 3 x^{3} - 6 x^{2} + 9