Derivative of y=sin(7-5x)

1. Let $u = 7 - 5 x$.

2. The derivative of sine is cosine:

   $$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$$

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

   1. Differentiate $7 - 5 x$ term by term:

      1. The derivative of the constant $7$ is zero.

      2. 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: $5$

         So, the result is: $-5$

      The result is: $-5$

   The result of the chain rule is:

   $$- 5 \cos{\left(5 x - 7 \right)}$$

The answer is:

$$- 5 \cos{\left(5 x - 7 \right)}$$