Mister Exam

Derivative of x^3/x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

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 3
x 
--
x 
x3x\frac{x^{3}}{x}
x^3/x
Detail solution
  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=x3f{\left(x \right)} = x^{3} and g(x)=xg{\left(x \right)} = x.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    Now plug in to the quotient rule:

    2x2 x


The answer is:

2x2 x

The graph
02468-8-6-4-2-1010200-100
The first derivative [src]
2*x
2x2 x
The second derivative [src]
2
22
The third derivative [src]
0
00
The graph
Derivative of x^3/x