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Derivative of:
Derivative of tanh(x)
Derivative of e^x*(2*x-3)
Derivative of cos²x
Derivative of 9x-9ln(x+11)+7
Identical expressions
e^x*(two *x- three)
e to the power of x multiply by (2 multiply by x minus 3)
e to the power of x multiply by (two multiply by x minus three)
ex*(2*x-3)
ex*2*x-3
e^x(2x-3)
ex(2x-3)
ex2x-3
e^x2x-3
Similar expressions
e^x*(2*x+3)

The derivative of the function/ e^x*(2*x-3)

Derivative of e^x(2x-3)

The solution

You have entered [src]

 x          
E *(2*x - 3)

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

E^x*(2*x - 3)

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.
$g{\left(x \right)} = 2 x - 3$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $2 x - 3$ 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: $2$
  2. The derivative of the constant $-3$ is zero.
  The result is: $2$
The result is: $\left(2 x - 3\right) e^{x} + 2 e^{x}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x              x
2*e  + (2*x - 3)*e

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

Simplify

The second derivative [src]

           x
(1 + 2*x)*e

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

Simplify

The third derivative [src]

           x
(3 + 2*x)*e

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

Simplify

The graph

Derivative of e^x*(2*x-3)