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Derivative of:
Derivative of y=2^x
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Identical expressions
three *e^(five *x)+ two
3 multiply by e to the power of (5 multiply by x) plus 2
three multiply by e to the power of (five multiply by x) plus two
3*e(5*x)+2
3*e5*x+2
3e^(5x)+2
3e(5x)+2
3e5x+2
3e^5x+2
Similar expressions
3*e^(5*x)-2

The derivative of the function/ 3*e^(5*x)+2

Derivative of 3e^(5x)+2

The solution

You have entered [src]

   5*x    
3*e    + 2

$$3 e^{5 x} + 2$$

d /   5*x    \
--\3*e    + 2/
dx

$$\frac{d}{d x} \left(3 e^{5 x} + 2\right)$$

Transform

Detail solution

Differentiate $3 e^{5 x} + 2$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 5 x$ .
  2. The derivative of $e^{u}$ is itself.
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x$ :
    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: $5$
    The result of the chain rule is:
    
    $5 e^{5 x}$
  So, the result is: $15 e^{5 x}$
2. The derivative of the constant $2$ is zero.
The result is: $15 e^{5 x}$

The answer is:

$15 e^{5 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    5*x
15*e

$$15 e^{5 x}$$

Simplify

The second derivative [src]

    5*x
75*e

$$75 e^{5 x}$$

Simplify

The third derivative [src]

     5*x
375*e

$$375 e^{5 x}$$

Simplify

The graph

Derivative of 3*e^(5*x)+2