展开 (f(x+h)-f(7x^2-6))/h

解答

展开

\frac{f ( x + h ) - f ( 7 x ^{2} - 6 )}{h}

\frac{f x}{h} + f - \frac{7 f x ^{2}}{h} + \frac{6 f}{h}

求解步骤

\frac{f ( x + h ) - f ( 7 x ^{2} - 6 )}{h}

乘开

f (x + h) - f (7 x^{2} - 6) : f x + f h - 7 f x^{2} + 6 f

= \frac{f x + f h - 7 f x ^{2} + 6 f}{h}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{f x + f h - 7 f x ^{2} + 6 f}{h} = \frac{f x}{h} + \frac{f h}{h} - \frac{7 f x ^{2}}{h} + \frac{6 f}{h}

= \frac{f x}{h} + \frac{f h}{h} - \frac{7 f x ^{2}}{h} + \frac{6 f}{h}

消掉

\frac{f h}{h} : f

= \frac{f x}{h} + f - \frac{7 f x ^{2}}{h} + \frac{6 f}{h}

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