How do you differentiate $f(x)= (9-x)(5/x^2 -4)$ using the product rule?

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Answer 1 · 2015-12-24T12:34:13

The product rule states that for $y=f(x)g(x)$ , then $(dy)/(dx)=f'(x)g(x)+f(x)g'(x)$

Remembering the power rule that states $a^-n=1/(a^n)$ , we can rewrite it as follows

$f(x)=(9-x)(5x^-2-4)$

$(df(x))=(-1)(5x^-2-4)+(9-x)(-10x^-3)$

$(df(x))/(dx)=(4-5x^-2)+(-90x^-3+10x^-2)$

$(df(x))/(dx)=4+5x^-2-90x^-3$

or, if you prefer,

$(df(x))/(dx)=4+5/x^2-90/x^3$

How do you differentiate f(x)= (9-x)(5/x^2 -4) f(x)= (9-x)(5/x^2 -4) using the product rule?