derivative (sqrt(9-x^2))(1/3)pix^2

解答

导数

(9 - x^{2}) (\frac{1}{3}) π x^{2}

\frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

求解步骤

\frac{d}{d x} (9 - x^{2} \frac{1}{3} π x^{2})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} π \frac{d}{d x} (9 - x^{2} x^{2})

使用微分乘法定则:

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

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

= \frac{1}{3} π (\frac{d}{d x} (9 - x^{2}) x^{2} + \frac{d}{d x} (x^{2}) 9 - x^{2})

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

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

= \frac{1}{3} π ((- \frac{x}{9 - x ^{2}}) x^{2} + 2 x 9 - x^{2})

化简

\frac{1}{3} π ((- \frac{x}{9 - x ^{2}}) x^{2} + 2 x 9 - x^{2}) : \frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

= \frac{π x ( - x ^{2} + 6 )}{9 - x ^{2}}

t an g e n t f (x) = (- 3 x^{2} + 3) e^{2 x}, at x = 2

\int \frac{1}{3 + x ^{2}} d x

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

\int_{- 1}^{1} 2 ∣ x ∣ d x

d er i v a t i v e 5 + \frac{6}{x} + \frac{6}{x ^{2}}