derivative of (x^2-10x+9sqrt(25-x^2))

解答

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

\frac{- 3 x ^{3} + 20 x ^{2} + 41 x - 250}{25 - x ^{2}}

求解步骤

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

使用微分乘法定则:

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

f = x^{2} - 10 x + 9, g = 25 - x^{2}

= \frac{d}{d x} (x^{2} - 10 x + 9) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) (x^{2} - 10 x + 9)

\frac{d}{d x} (x^{2} - 10 x + 9) = 2 x - 10

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= (2 x - 10) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 10 x + 9)

化简

(2 x - 10) 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) (x^{2} - 10 x + 9) : \frac{- 3 x ^{3} + 20 x ^{2} + 41 x - 250}{25 - x ^{2}}

= \frac{- 3 x ^{3} + 20 x ^{2} + 41 x - 250}{25 - x ^{2}}

\int (x cos^{2} (y) - sin (y)) d x

\int [cos (\frac{x}{2}) - sin (3 \frac{x}{2})] d x

\frac{d}{d x} (\frac{7}{x ^{- 2}} + \frac{5}{x ^{- 3}})

a re a x, \frac{1}{3} x, x = 25

x \to 0 lim (\frac{100}{2})