derivative of y^2(8-x)

解答

\frac{d}{d x} (y^{2} (8 - x))

2 y \frac{d y}{d x} (8 - x) - y^{2}

求解步骤

\frac{d}{d x} (y^{2} (8 - x))

使用微分乘法定则:

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

f = y^{2}, g = 8 - x

= \frac{d}{d x} (y^{2}) (8 - x) + \frac{d}{d x} (8 - x) y^{2}

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

\frac{d}{d x} (8 - x) = - 1

= 2 y \frac{d y}{d x} (8 - x) + (- 1) y^{2}

化简

= 2 y \frac{d y}{d x} (8 - x) - y^{2}

x^{2} y^{^{'}} = 4 x^{2} y^{3} - 2 x y

n = 1 \sum \infty \frac{( 3 ^{n} )}{n !}

l a pl a ce t r an s f or m cos (4 t) cos (6 t)

\int 5 sin^{3} (x) cos (x) d x

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