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

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

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

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The solution

You have entered [src] 
  -2*y     
-e         
------- - y
   2
−y+(−1)e−2y2- y + \frac{\left(-1\right) e^{- 2 y}}{2} 
(-exp(-2*y))/2 - y
Detail solution

  1. Differentiate −y+(−1)e−2y2- 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=−2yu = - 2 y.

        2. The derivative of eue^{u} is itself.

        3. Then, apply the chain rule. Multiply by ddy(−2y)\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.

            1. Apply the power rule: yy goes to 11

            So, the result is: −2-2

          The result of the chain rule is:

          −2e−2y- 2 e^{- 2 y}

        So, the result is: 2e−2y2 e^{- 2 y}

      So, the result is: e−2ye^{- 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: yy goes to 11

      So, the result is: −1-1

    The result is: −1+e−2y-1 + e^{- 2 y}

The answer is:

−1+e−2y-1 + e^{- 2 y}

The graph
02468-8-6-4-2-1010-500000000500000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      -2*y
-1 + e
−1+e−2y-1 + e^{- 2 y}
Simplify
The second derivative [src] 
    -2*y
-2*e
−2e−2y- 2 e^{- 2 y}
Simplify
The third derivative [src] 
   -2*y
4*e
4e−2y4 e^{- 2 y}
Simplify
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