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Sum of series:
n^2*x^(n-1)
Identical expressions
n^ two *x^(n- one)
n squared multiply by x to the power of (n minus 1)
n to the power of two multiply by x to the power of (n minus one)
n2*x(n-1)
n2*xn-1
n²*x^(n-1)
n to the power of 2*x to the power of (n-1)
n^2x^(n-1)
n2x(n-1)
n2xn-1
n^2x^n-1
Similar expressions
n^2*x^(n+1)

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

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

The solution

You have entered [src]

 2  n - 1
n *x

$$n^{2} x^{n - 1}$$

n^2*x^(n - 1)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $x^{n - 1}$ goes to $\frac{x^{n - 1} \left(n - 1\right)}{x}$
So, the result is: $\frac{n^{2} x^{n - 1} \left(n - 1\right)}{x}$
Now simplify:

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

The answer is:

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

The first derivative [src]

 2  n - 1        
n *x     *(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

$$\frac{n^{2} x^{n - 1} \left(n - 2\right) \left(n - 1\right)}{x^{2}}$$

Simplify

The third derivative [src]

 2  -1 + n          /            2      \
n *x      *(-1 + n)*\5 + (-1 + n)  - 3*n/
-----------------------------------------
                     3                   
                    x

$$\frac{n^{2} x^{n - 1} \left(n - 1\right) \left(- 3 n + \left(n - 1\right)^{2} + 5\right)}{x^{3}}$$

Simplify

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

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The solution