Derivative of y=(3sin7x)/7

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. Let $u = 7 x$.

      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 $\frac{d}{d x} 7 x$:

         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: $7$

         The result of the chain rule is:

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

      So, the result is: $21 \cos{\left(7 x \right)}$

   So, the result is: $3 \cos{\left(7 x \right)}$

The answer is:

$$3 \cos{\left(7 x \right)}$$