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Derivative of:
Derivative of 2x²
Derivative of x^2*sqrt(1-x^2)
Derivative of y=3x²+5x+4
Derivative of x^3*cot(x)
Identical expressions
(-exp(- two *y))/ two -y
( minus exponent of ( minus 2 multiply by y)) divide by 2 minus y
( minus exponent of ( minus two multiply by y)) divide by two minus y
(-exp(-2y))/2-y
-exp-2y/2-y
(-exp(-2*y)) divide by 2-y
Similar expressions
(-exp(2*y))/2-y
(-exp(-2*y))/2+y
(exp(-2*y))/2-y

The derivative of the function/ (-exp(-2*y))/2-y

Derivative of (-exp(-2*y))/2-y

The solution

You have entered [src]

  -2*y     
-e         
------- - y
   2

$$- y + \frac{\left(-1\right) e^{- 2 y}}{2}$$

(-exp(-2*y))/2 - y

Detail solution

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

The answer is:

$-1 + e^{- 2 y}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -2*y
-1 + e

$$-1 + e^{- 2 y}$$

Simplify

The second derivative [src]

    -2*y
-2*e

$$- 2 e^{- 2 y}$$

Simplify

The third derivative [src]

   -2*y
4*e

$$4 e^{- 2 y}$$

Simplify