Derivative of exp(3*x/4)

1. Let $u = \frac{3 x}{4}$.

2. The derivative of $e^{u}$ is itself.

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{3 x}{4}$:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      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: $3$

      So, the result is: $\frac{3}{4}$

   The result of the chain rule is:

   $$\frac{3 e^{\frac{3 x}{4}}}{4}$$

4. Now simplify:

   $$\frac{3 e^{\frac{3 x}{4}}}{4}$$

The answer is:

$$\frac{3 e^{\frac{3 x}{4}}}{4}$$