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Derivative of:
Derivative of y=cos9x
Derivative of (x+2)*(x^2-4*x+5)
Derivative of (x^2+8)/(x-1)
Derivative of x^2-4x/x^3-2x^2
Identical expressions
exp(ax)/((p- one)(p- two))
exponent of (ax) divide by ((p minus 1)(p minus 2))
exponent of (ax) divide by ((p minus one)(p minus two))
expax/p-1p-2
exp(ax) divide by ((p-1)(p-2))
Similar expressions
exp(ax)/((p+1)(p-2))
exp(ax)/((p-1)(p+2))

The derivative of the function/ exp(ax)/((p-1)(p-2))

Derivative of exp(ax)/((p-1)(p-2))

The solution

You have entered [src]

       a*x     
      e        
---------------
(p - 1)*(p - 2)

$$\frac{e^{a x}}{\left(p - 2\right) \left(p - 1\right)}$$

exp(a*x)/(((p - 1)*(p - 2)))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = a x$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} a x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $a$
  The result of the chain rule is:
  
  $a e^{a x}$
So, the result is: $a \frac{1}{\left(p - 2\right) \left(p - 1\right)} e^{a x}$
Now simplify:

$\frac{a e^{a x}}{\left(p - 2\right) \left(p - 1\right)}$

The answer is:

$\frac{a e^{a x}}{\left(p - 2\right) \left(p - 1\right)}$

The first derivative [src]

         1         a*x
a*---------------*e   
  (p - 1)*(p - 2)

$$a \frac{1}{\left(p - 2\right) \left(p - 1\right)} e^{a x}$$

Simplify

The second derivative [src]

      2  a*x     
     a *e        
-----------------
(-1 + p)*(-2 + p)

$$\frac{a^{2} e^{a x}}{\left(p - 2\right) \left(p - 1\right)}$$

Simplify

The third derivative [src]

      3  a*x     
     a *e        
-----------------
(-1 + p)*(-2 + p)

$$\frac{a^{3} e^{a x}}{\left(p - 2\right) \left(p - 1\right)}$$

Simplify