Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^2*e^2
Derivative of x^3+2*x^5
Derivative of (4-3*x)^7
Derivative of 7*x+4
Identical expressions
y=e^x*(x+ four)
y equally e to the power of x multiply by (x plus 4)
y equally e to the power of x multiply by (x plus four)
y=ex*(x+4)
y=ex*x+4
y=e^x(x+4)
y=ex(x+4)
y=exx+4
y=e^xx+4
Similar expressions
y=e^x*(x-4)

The derivative of the function/ y=e^x*(x+4)

Derivative of y=e^x*(x+4)

The solution

You have entered [src]

 x        
E *(x + 4)

$$e^{x} \left(x + 4\right)$$

E^x*(x + 4)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
$g{\left(x \right)} = x + 4$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 4$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $4$ is zero.
  The result is: $1$
The result is: $e^{x} + \left(x + 4\right) e^{x}$
Now simplify:

$\left(x + 5\right) e^{x}$

The answer is:

$\left(x + 5\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x            x
E  + (x + 4)*e

$$e^{x} + \left(x + 4\right) e^{x}$$

Simplify

The second derivative [src]

         x
(6 + x)*e

$$\left(x + 6\right) e^{x}$$

Simplify

The third derivative [src]

         x
(7 + x)*e

$$\left(x + 7\right) e^{x}$$

Simplify

The graph

Derivative of y=e^x*(x+4)