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Derivative of:
Derivative of (5*x-4)*(2*x^4-7*x+1)
Derivative of x/5+5/x
Derivative of (x+5)^2*(x-1)+7
Derivative of x^3-48x+17
Identical expressions
four -exp^(-(x^ two))
4 minus exponent of to the power of ( minus (x squared ))
four minus exponent of to the power of ( minus (x to the power of two))
4-exp(-(x2))
4-exp-x2
4-exp^(-(x²))
4-exp to the power of (-(x to the power of 2))
4-exp^-x^2
Similar expressions
4-exp^((x^2))
4+exp^(-(x^2))

The derivative of the function/ 4-exp^(-(x^2))

Derivative of 4-exp^(-(x^2))

The solution

You have entered [src]

       2
     -x 
4 - E

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

4 - E^(-x^2)

Detail solution

Differentiate $4 - e^{- x^{2}}$ term by term:
1. The derivative of the constant $4$ is zero.
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = - x^{2}$ .
  2. The derivative of $e^{u}$ is itself.
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- x^{2}\right)$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      So, the result is: $- 2 x$
    The result of the chain rule is:
    
    $- 2 x e^{- x^{2}}$
  So, the result is: $2 x e^{- x^{2}}$
The result is: $2 x e^{- x^{2}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2
     -x 
2*x*e

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

                   2
    /        2\  -x 
4*x*\-3 + 2*x /*e

$$4 x \left(2 x^{2} - 3\right) e^{- x^{2}}$$

Simplify