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`1.f(x)=(x^3-6)/(x^2)` Find the Derivative of Function.``2.f(x)=`root(3)(x)+root(5)(x)`
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High School Teacher
To take the derivative of the function, apply the quotient rule `(u/v)'=(v*u'-u*v')/v^2` .
So, let `u = x^3 - 6` and `v=x^2` .
Then, take the derivative of u and v.
`u'=(x^3-6)'=(x^3)'-6' = 3x^2-0=3x^2`
And, plug-in u, v, u' and v' to the formula.
`f'(x)= ((x^3-6)/x^2)' = (x^2*3x^2-(x^3-6)*2x)/(x^2)^2`
Next, simplify f'(x).
Hence, the derivative of `f(x)= (x^3-6)/x^2` is `f'(x)=(x^3+12)/x^3` .
Posted by mjripalda on February 15, 2013 at 2:45 AM (Answer #1)
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