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1/x^3
The derivative of the function/ 1/x^3

Derivative of 1/x^3

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

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from to

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The solution

You have entered [src] 
  1 
1*--
   3
  x
1⋅1x31 \cdot \frac{1}{x^{3}} 
d /  1 \
--|1*--|
dx|   3|
  \  x /
ddx1⋅1x3\frac{d}{d x} 1 \cdot \frac{1}{x^{3}}
Transform
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)=1f{\left(x \right)} = 1 and g(x)=x3g{\left(x \right)} = x^{3}.

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

    1. The derivative of the constant 11 is zero.

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

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

    Now plug in to the quotient rule:

    −3x4- \frac{3}{x^{4}}

The answer is:

−3x4- \frac{3}{x^{4}}

The graph
02468-8-6-4-2-1010-5000050000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-3  
----
   3
x*x
−3xx3- \frac{3}{x x^{3}}
Simplify
The second derivative [src] 
12
--
 5
x
12x5\frac{12}{x^{5}}
Simplify
The third derivative [src] 
-60 
----
  6 
 x
−60x6- \frac{60}{x^{6}}
Simplify
The graph
Derivative of 1/x^3
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