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Find 
(d)/(dx)(sin(-2x+7))
Answer:

Find ddx(sin(2x+7)) \frac{d}{d x}(\sin (-2 x+7)) \newlineAnswer:

Full solution

Q. Find ddx(sin(2x+7)) \frac{d}{d x}(\sin (-2 x+7)) \newlineAnswer:
  1. Identify Composite Function: We need to find the derivative of the function sin(2x+7)\sin(-2x+7) with respect to xx. We will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. The outer function in this case is sin(u)\sin(u), and the inner function is u=2x+7u = -2x + 7.
  2. Derivative of Outer Function: First, we find the derivative of the outer function with respect to its argument uu. The derivative of sin(u)\sin(u) with respect to uu is cos(u)\cos(u).
  3. Derivative of Inner Function: Next, we find the derivative of the inner function 2x+7-2x + 7 with respect to xx. The derivative of 2x-2x with respect to xx is 2-2, and the derivative of a constant like 77 is 00.
  4. Apply Chain Rule: Now we apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us cos(2x+7)(2)\cos(-2x + 7) \cdot (-2).
  5. Simplify Final Answer: Simplify the expression to get the final answer. The derivative of sin(2x+7)\sin(-2x+7) with respect to xx is 2cos(2x+7)-2 \cdot \cos(-2x + 7).

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