derivative of {f}(x(x)^{-1}(x^2))

解答

\frac{d}{d x} (f (x) (x)^{- 1} (x^{2}))

f (x) + x \frac{d}{d x} (f (x))

求解步骤

\frac{d}{d x} (f (x) (x)^{- 1} (x^{2}))

化简

f (x) (x)^{- 1} (x^{2}) : x f (x)

= \frac{d}{d x} (x f (x))

使用微分乘法定则:

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

f = x, g = f (x)

= \frac{d x}{d x} f (x) + \frac{d}{d x} (f (x)) x

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

= 1 \cdot f (x) + \frac{d}{d x} (f (x)) x

化简

= f (x) + x \frac{d}{d x} (f (x))

\int_{0}^{1} π (5 x^{2})^{2} d x

\int x - csc (x) cot (x) d x

\int (sin (7 x)) d x

\frac{d}{d x} (\frac{1}{2} ln (2 x))

\frac{d y}{d t} = (15 - \frac{3 y}{360 - 2 t})