derivative of 8xy-1/4 (x+y^4)

解答

\frac{d}{d x} (8 x y - \frac{1}{4} (x + y)^{4})

8 (y + x \frac{d y}{d x}) - (1 + \frac{d y}{d x}) (x + y)^{3}

求解步骤

\frac{d}{d x} (8 x y - \frac{1}{4} (x + y)^{4})

化简

8 x y - \frac{1}{4} (x + y)^{4} : 8 x y - \frac{( x + y ) ^{4}}{4}

= \frac{d}{d x} (8 x y - \frac{( x + y ) ^{4}}{4})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (8 x y) - \frac{d}{d x} (\frac{( x + y ) ^{4}}{4})

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

\frac{d}{d x} (\frac{( x + y ) ^{4}}{4}) = (1 + \frac{d y}{d x}) (x + y)^{3}

= 8 (y + x \frac{d y}{d x}) - (1 + \frac{d y}{d x}) (x + y)^{3}

f (x) = x^{2} cos (x^{2})

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