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Derivative of:
Derivative of e^(-x^2)
Derivative of x^x^2
Derivative of -e^-x
Derivative of (x)^(1/2)
Identical expressions
e^(four *x- three *x)
e to the power of (4 multiply by x minus 3 multiply by x)
e to the power of (four multiply by x minus three multiply by x)
e(4*x-3*x)
e4*x-3*x
e^(4x-3x)
e(4x-3x)
e4x-3x
e^4x-3x
Similar expressions
e^(4*x+3*x)

The derivative of the function/ e^(4*x-3*x)

Derivative of e^(4x-3x)

The solution

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 4*x - 3*x
E

$$e^{- 3 x + 4 x}$$

E^(4*x - 3*x)

Detail solution

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

$e^{- 3 x + 4 x}$
Now simplify:

$e^{x}$

The answer is:

$e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 4*x - 3*x
E

$$e^{- 3 x + 4 x}$$

Simplify

The second derivative [src]

x
e

$$e^{x}$$

Simplify

The third derivative [src]

x
e

$$e^{x}$$

Simplify