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Derivative of:
Derivative of (x^2+1)^3
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Derivative of 4*x^4
Identical expressions
y=e^(3x^ two)+ one
y equally e to the power of (3x squared ) plus 1
y equally e to the power of (3x to the power of two) plus one
y=e(3x2)+1
y=e3x2+1
y=e^(3x²)+1
y=e to the power of (3x to the power of 2)+1
y=e^3x^2+1
Similar expressions
y=e^(3x^2)-1

The derivative of the function/ y=e^(3x^2)+1

Derivative of y=e^(3x^2)+1

The solution

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    2    
 3*x     
e     + 1

$$e^{3 x^{2}} + 1$$

  /    2    \
d | 3*x     |
--\e     + 1/
dx

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

Transform

Detail solution

Differentiate $e^{3 x^{2}} + 1$ term by term:
1. Let $u = 3 x^{2}$ .
2. The derivative of $e^{u}$ is itself.
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x^{2}$ :
  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: $6 x$
  The result of the chain rule is:
  
  $6 x e^{3 x^{2}}$
4. The derivative of the constant $1$ is zero.
The result is: $6 x e^{3 x^{2}}$

The answer is:

$6 x e^{3 x^{2}}$

The graph

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The first derivative [src]

        2
     3*x 
6*x*e

$$6 x e^{3 x^{2}}$$

Simplify

The second derivative [src]

                 2
  /       2\  3*x 
6*\1 + 6*x /*e

$$6 \cdot \left(6 x^{2} + 1\right) e^{3 x^{2}}$$

Simplify

The third derivative [src]

                     2
      /       2\  3*x 
108*x*\1 + 2*x /*e

$$108 x \left(2 x^{2} + 1\right) e^{3 x^{2}}$$

Simplify

The graph

Derivative of y=e^(3x^2)+1