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Derivative of:
Derivative of f(x)=x^2
Derivative of y=2x+3
Derivative of x^(5*x)
Derivative of x^3/(x^2-x+1)
Identical expressions
4x+e^x^ two - five
4x plus e to the power of x squared minus 5
4x plus e to the power of x to the power of two minus five
4x+ex2-5
4x+e^x²-5
4x+e to the power of x to the power of 2-5
Similar expressions
4x-e^x^2-5
4x+e^x^2+5

The derivative of the function/ 4x+e^x^2-5

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

The solution

You have entered [src]

       / 2\    
       \x /    
4*x + e     - 5

4 x + e^{x^{2}} - 5

  /       / 2\    \
d |       \x /    |
--\4*x + e     - 5/
dx

\frac{d}{d x} \left(4 x + e^{x^{2}} - 5\right)

Transform

Detail solution

Differentiate $4 x + e^{x^{2}} - 5$ 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: $x$ goes to $1$
  So, the result is: $4$
2. Let $u = x^{2}$ .
3. The derivative of $e^{u}$ is itself.
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  The result of the chain rule is:
  
  $2 x e^{x^{2}}$
5. The derivative of the constant $\left(-1\right) 5$ is zero.
The result is: $2 x e^{x^{2}} + 4$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

2 \cdot \left(2 x^{2} + 1\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

The graph

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