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Derivative of:
Derivative of c
Derivative of atan(2/x)
Derivative of asin((x-1)/x)
Derivative of asin(sin(t)/cos(t))
Identical expressions
three *(exp(one))^(-2x)
3 multiply by ( exponent of (1)) to the power of ( minus 2x)
three multiply by ( exponent of (one)) to the power of ( minus 2x)
3*(exp(1))(-2x)
3*exp1-2x
3(exp(1))^(-2x)
3(exp(1))(-2x)
3exp1-2x
3exp1^-2x
Similar expressions
3*(exp(1))^(2x)

The derivative of the function/ 3*(exp(1))^(-2x)

Derivative of 3*(exp(1))^(-2x)

The solution

You have entered [src]

      -2*x
  / 1\    
3*\e /

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

3*exp(1)^(-2*x)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = - 2 x$ .
2. $\frac{d}{d u} e^{u} = e^{u}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 2 x\right)$ :
  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: $-2$
  The result of the chain rule is:
  
  $- 2 e^{- 2 x}$
So, the result is: $- 6 e^{- 2 x}$

The answer is:

$- 6 e^{- 2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -2*x
-6*e

$$- 6 e^{- 2 x}$$

Simplify

The second derivative [src]

    -2*x
12*e

$$12 e^{- 2 x}$$

Simplify

The third derivative [src]

     -2*x
-24*e

$$- 24 e^{- 2 x}$$

Simplify