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The derivative of the function/ n^2*x^(n-1)

Derivative of n^2*x^(n-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2  n - 1
n *x
n2xn−1n^{2} x^{n - 1} 
n^2*x^(n - 1)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the power rule: xn−1x^{n - 1} goes to xn−1(n−1)x\frac{x^{n - 1} \left(n - 1\right)}{x}

    So, the result is: n2xn−1(n−1)x\frac{n^{2} x^{n - 1} \left(n - 1\right)}{x}

  2. Now simplify:

    n2xn−2(n−1)n^{2} x^{n - 2} \left(n - 1\right)

The answer is:

n2xn−2(n−1)n^{2} x^{n - 2} \left(n - 1\right)

The first derivative [src] 
 2  n - 1        
n *x     *(n - 1)
-----------------
        x
n2xn−1(n−1)x\frac{n^{2} x^{n - 1} \left(n - 1\right)}{x}
Simplify
The second derivative [src] 
 2  -1 + n                  
n *x      *(-1 + n)*(-2 + n)
----------------------------
              2             
             x
n2xn−1(n−2)(n−1)x2\frac{n^{2} x^{n - 1} \left(n - 2\right) \left(n - 1\right)}{x^{2}}
Simplify
The third derivative [src] 
 2  -1 + n          /            2      \
n *x      *(-1 + n)*\5 + (-1 + n)  - 3*n/
-----------------------------------------
                     3                   
                    x
n2xn−1(n−1)(−3n+(n−1)2+5)x3\frac{n^{2} x^{n - 1} \left(n - 1\right) \left(- 3 n + \left(n - 1\right)^{2} + 5\right)}{x^{3}}
Simplify
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