Derivative of e^((7x-1)/5)

1. Let $u = \frac{7 x - 1}{5}$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{7 x - 1}{5}$:

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

      1. Differentiate $7 x - 1$ 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: $7$

         2. The derivative of the constant $\left(-1\right) 1$ is zero.

         The result is: $7$

      So, the result is: $\frac{7}{5}$

   The result of the chain rule is:

   $$\frac{7 e^{\frac{7 x - 1}{5}}}{5}$$

4. Now simplify:

   $$\frac{7 e^{\frac{7 x}{5} - \frac{1}{5}}}{5}$$

The answer is:

$$\frac{7 e^{\frac{7 x}{5} - \frac{1}{5}}}{5}$$