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y=(2x^-3x^2)
The derivative of the function/ y=(2x^-3x^2)

You entered:

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

What you mean?

2*x^2/x^3
 
2*x^((-3*x)^2)
 
2*x^((-3*x)^2)

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

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

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Piecewise:

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}}
Transform
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-2 
---
  2
 x
−2x2- \frac{2}{x^{2}}
Simplify
The second derivative [src] 
4 
--
 3
x
4x3\frac{4}{x^{3}}
Simplify
The third derivative [src] 
-12 
----
  4 
 x
−12x4- \frac{12}{x^{4}}
Simplify
The graph
Derivative of y=(2x^-3x^2)
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