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y=(2x^-3x^2)

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y=(2x^-3x^2)

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Derivative of y=(2x^-3x^2)

Function f() - derivative -N order at the point
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The graph:

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The solution

You have entered [src]
   2
2*x 
----
  3 
 x  
2x2x3\frac{2 x^{2}}{x^{3}}
  /   2\
d |2*x |
--|----|
dx|  3 |
  \ x  /
ddx2x2x3\frac{d}{d x} \frac{2 x^{2}}{x^{3}}
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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)=x2f{\left(x \right)} = x^{2} and g(x)=x3g{\left(x \right)} = x^{3}.

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

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      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:

      1x2- \frac{1}{x^{2}}

    So, the result is: 2x2- \frac{2}{x^{2}}


The answer is:

2x2- \frac{2}{x^{2}}

The graph
02468-8-6-4-2-1010-250250
The first derivative [src]
-2 
---
  2
 x 
2x2- \frac{2}{x^{2}}
The second derivative [src]
4 
--
 3
x 
4x3\frac{4}{x^{3}}
The third derivative [src]
-12 
----
  4 
 x  
12x4- \frac{12}{x^{4}}
The graph
Derivative of y=(2x^-3x^2)