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Identical expressions
exp^(x^ two - one)+ two *x^(two)*exp^(x^ two - one)
exponent of to the power of (x squared minus 1) plus 2 multiply by x to the power of (2) multiply by exponent of to the power of (x squared minus 1)
exponent of to the power of (x to the power of two minus one) plus two multiply by x to the power of (two) multiply by exponent of to the power of (x to the power of two minus one)
exp(x2-1)+2*x(2)*exp(x2-1)
expx2-1+2*x2*expx2-1
exp^(x²-1)+2*x^(2)*exp^(x²-1)
exp to the power of (x to the power of 2-1)+2*x to the power of (2)*exp to the power of (x to the power of 2-1)
exp^(x^2-1)+2x^(2)exp^(x^2-1)
exp(x2-1)+2x(2)exp(x2-1)
expx2-1+2x2expx2-1
exp^x^2-1+2x^2exp^x^2-1
Similar expressions
exp^(x^2-1)+2*x^(2)*exp^(x^2+1)
exp^(x^2-1)-2*x^(2)*exp^(x^2-1)
exp^(x^2+1)+2*x^(2)*exp^(x^2-1)

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

Derivative of exp^(x^2-1)+2x^(2)exp^(x^2-1)

The solution

You have entered [src]

  2              2    
 x  - 1      2  x  - 1
E       + 2*x *E

$$e^{x^{2} - 1} \cdot 2 x^{2} + e^{x^{2} - 1}$$

E^(x^2 - 1) + (2*x^2)*E^(x^2 - 1)

Detail solution

Differentiate $e^{x^{2} - 1} \cdot 2 x^{2} + e^{x^{2} - 1}$ term by term:
1. Let $u = x^{2} - 1$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 1\right)$ :
  1. Differentiate $x^{2} - 1$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of the constant $-1$ is zero.
    The result is: $2 x$
  The result of the chain rule is:
  
  $2 x e^{x^{2} - 1}$
4. Apply the product rule:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = 2 x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  $g{\left(x \right)} = e^{x^{2} - 1}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Let $u = x^{2} - 1$ .
  2. The derivative of $e^{u}$ is itself.
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 1\right)$ :
    1. Differentiate $x^{2} - 1$ term by term:
      1. Apply the power rule: $x^{2}$ goes to $2 x$
      2. The derivative of the constant $-1$ is zero.
      The result is: $2 x$
    The result of the chain rule is:
    
    $2 x e^{x^{2} - 1}$
  The result is: $4 x^{3} e^{x^{2} - 1} + 4 x e^{x^{2} - 1}$
The result is: $4 x^{3} e^{x^{2} - 1} + 6 x e^{x^{2} - 1}$
Now simplify:

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

The answer is:

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

The graph

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The first derivative [src]

       2             2    
   3  x  - 1        x  - 1
4*x *e       + 6*x*e

$$4 x^{3} e^{x^{2} - 1} + 6 x e^{x^{2} - 1}$$

Simplify

The second derivative [src]

                            2
  /       4       2\  -1 + x 
2*\3 + 4*x  + 12*x /*e

$$2 \left(4 x^{4} + 12 x^{2} + 3\right) e^{x^{2} - 1}$$

Simplify

The third derivative [src]

                               2
    /        4       2\  -1 + x 
4*x*\15 + 4*x  + 20*x /*e

$$4 x \left(4 x^{4} + 20 x^{2} + 15\right) e^{x^{2} - 1}$$

Simplify

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Derivative of exp^(x^2-1)+2x^(2)exp^(x^2-1)

The graph:

Piecewise:

The solution

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

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Piecewise:

The solution

Derivative of exp^(x^2-1)+2x^(2)exp^(x^2-1)