Mister Exam

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

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

The solution

You have entered [src]

 x*(-3)
E

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

E^(x*(-3))

Detail solution

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

$- 3 e^{\left(-3\right) x}$
Now simplify:

$- 3 e^{- 3 x}$

The answer is:

$- 3 e^{- 3 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    x*(-3)
-3*e

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

Simplify

The second derivative [src]

   -3*x
9*e

$$9 e^{- 3 x}$$

Simplify

The third derivative [src]

     -3*x
-27*e

$$- 27 e^{- 3 x}$$

Simplify

The graph

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