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4x+e^x^2-5

Derivative of 4x+e^x^2-5

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

The graph:

from to

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The solution

You have entered [src]
       / 2\    
       \x /    
4*x + e     - 5
4x+ex254 x + e^{x^{2}} - 5
  /       / 2\    \
d |       \x /    |
--\4*x + e     - 5/
dx                 
ddx(4x+ex25)\frac{d}{d x} \left(4 x + e^{x^{2}} - 5\right)
Detail solution
  1. Differentiate 4x+ex254 x + e^{x^{2}} - 5 term by term:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: 44

    2. Let u=x2u = x^{2}.

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

    4. Then, apply the chain rule. Multiply by ddxx2\frac{d}{d x} x^{2}:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      The result of the chain rule is:

      2xex22 x e^{x^{2}}

    5. The derivative of the constant (1)5\left(-1\right) 5 is zero.

    The result is: 2xex2+42 x e^{x^{2}} + 4


The answer is:

2xex2+42 x e^{x^{2}} + 4

The graph
02468-8-6-4-2-10101e45-5e44
The first derivative [src]
         / 2\
         \x /
4 + 2*x*e    
2xex2+42 x e^{x^{2}} + 4
The second derivative [src]
              / 2\
  /       2\  \x /
2*\1 + 2*x /*e    
2(2x2+1)ex22 \cdot \left(2 x^{2} + 1\right) e^{x^{2}}
The third derivative [src]
                / 2\
    /       2\  \x /
4*x*\3 + 2*x /*e    
4x(2x2+3)ex24 x \left(2 x^{2} + 3\right) e^{x^{2}}
The graph
Derivative of 4x+e^x^2-5