derivative (y+3/y)(y^2-5)

解答

导数

(y + \frac{3}{y}) (y^{2} - 5)

3 y^{2} + \frac{15}{y ^{2}} - 2

求解步骤

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

使用微分乘法定则:

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

f = y + \frac{3}{y}, g = y^{2} - 5

= \frac{d}{d y} (y + \frac{3}{y}) (y^{2} - 5) + \frac{d}{d y} (y^{2} - 5) (y + \frac{3}{y})

\frac{d}{d y} (y + \frac{3}{y}) = 1 - \frac{3}{y ^{2}}

\frac{d}{d y} (y^{2} - 5) = 2 y

= (1 - \frac{3}{y ^{2}}) (y^{2} - 5) + 2 y (y + \frac{3}{y})

化简

(1 - \frac{3}{y ^{2}}) (y^{2} - 5) + 2 y (y + \frac{3}{y}) : 3 y^{2} + \frac{15}{y ^{2}} - 2

= 3 y^{2} + \frac{15}{y ^{2}} - 2

\frac{d}{d x} (sec^{n - 2} (x))

x \to 0 lim (\frac{1 0 ^{x} - 1}{x})

d er i v a t i v e (x^{4} + 2)^{2} (x^{5} + 4)^{4}

d er i v a t i v e x^{2} - 2 x + 5

\int_{- \infty}^{8} x e^{\frac{x}{4}} d x