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#