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Find 
(d)/(dx)(-cos(-x+5))
Answer:

Find ddx(cos(x+5)) \frac{d}{d x}(-\cos (-x+5)) \newlineAnswer:

Full solution

Q. Find ddx(cos(x+5)) \frac{d}{d x}(-\cos (-x+5)) \newlineAnswer:
  1. Identify Composite Function: We are asked to find the derivative of the function cos(x+5)-\cos(-x+5) with respect to xx. To do this, 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 cos(u)-\cos(u), where u=x+5u = -x + 5, and the inner function is u=x+5u = -x + 5.
  2. Find Derivative of Outer Function: First, we find the derivative of the outer function cos(u)-\cos(u) with respect to uu. The derivative of cos(u)\cos(u) with respect to uu is sin(u)-\sin(u), so the derivative of cos(u)-\cos(u) with respect to uu is sin(u)\sin(u).
  3. Find Derivative of Inner Function: Next, we find the derivative of the inner function u=x+5u = -x + 5 with respect to xx. The derivative of x-x with respect to xx is 1-1, and the derivative of a constant, like 55, is 00. So, the derivative of uu with respect to xx is 1-1.
  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 sin(u)(1)\sin(u) \cdot (-1), where u=x+5u = -x + 5.
  5. Substitute and Simplify: Substitute u=x+5u = -x + 5 into the expression sin(u)(1)\sin(u) \cdot (-1) to get the final derivative: sin(x+5)(1)\sin(-x + 5) \cdot (-1).
  6. Get Final Derivative: Simplify the expression to get the final answer. The final derivative is sin(x+5)-\sin(-x + 5).

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