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The derivative of the function/ 2*exp(-ax^b)

Derivative of 2*exp(-ax^b)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
       b
   -a*x 
2*e
$$2 e^{- a x^{b}}$$ 
2*exp((-a)*x^b)
Detail solution

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

    1. Let .

    2. The derivative of is itself.

    3. Then, apply the chain rule. Multiply by :

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

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    So, the result is:

  2. Now simplify:

The answer is:

The first derivative [src] 
               b
        b  -a*x 
-2*a*b*x *e     
----------------
       x
$$- \frac{2 a b x^{b} e^{- a x^{b}}}{x}$$
Simplify
The second derivative [src] 
                               b
       b /             b\  -a*x 
2*a*b*x *\1 - b + a*b*x /*e     
--------------------------------
                2               
               x
$$\frac{2 a b x^{b} \left(a b x^{b} - b + 1\right) e^{- a x^{b}}}{x^{2}}$$
Simplify
The third derivative [src] 
                                                                  b
        b /     2          2  2  2*b        2  b          b\  -a*x 
-2*a*b*x *\2 + b  - 3*b + a *b *x    - 3*a*b *x  + 3*a*b*x /*e     
-------------------------------------------------------------------
                                  3                                
                                 x
$$- \frac{2 a b x^{b} \left(a^{2} b^{2} x^{2 b} - 3 a b^{2} x^{b} + 3 a b x^{b} + b^{2} - 3 b + 2\right) e^{- a x^{b}}}{x^{3}}$$
Simplify
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