derivative of x^2sqrt(4x-9)

Lösung

\frac{d}{d x} (x^{2} 4 x - 9)

\frac{10 x ^{2} - 18 x}{4 x - 9}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 4 x - 9)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 4 x - 9

= \frac{d}{d x} (x^{2}) 4 x - 9 + \frac{d}{d x} (4 x - 9) x^{2}

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

\frac{d}{d x} (4 x - 9) = \frac{2}{4 x - 9}

= 2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2}

Vereinfache

2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2} : \frac{10 x ^{2} - 18 x}{4 x - 9}

= \frac{10 x ^{2} - 18 x}{4 x - 9}

\int - cos (u) + \frac{1}{3} cos^{3} (u) d u

d er i v a t i v e (3 x^{2} - 10)^{- 13}

\int (- 3 (\frac{9 x ^{2}}{2}) - 4 x^{3}) d x

y^{^{'}} = \frac{e ^{t}}{3 y ^{2}}

\int 22 tan^{21} (x) sec^{2} (x) d x