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y=e^(4x-5)

Derivative of y=e^(4x-5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 4*x - 5
E       
$$e^{4 x - 5}$$
E^(4*x - 5)
Detail solution
  1. Let .

  2. The derivative of is itself.

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

    1. Differentiate term by term:

      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:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   4*x - 5
4*e       
$$4 e^{4 x - 5}$$
The second derivative [src]
    -5 + 4*x
16*e        
$$16 e^{4 x - 5}$$
The third derivative [src]
    -5 + 4*x
64*e        
$$64 e^{4 x - 5}$$
The graph
Derivative of y=e^(4x-5)