Question
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Lse an appropriate method of
ifferentiation determine
ne following

Ask by Harris Li. in South Africa
Jan 22,2025

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Tutor-Verified Answer

Answer

To find the derivative of , use the chain rule multiple times:
  1. Differentiate the outer cosine function: .
  2. Differentiate the square root: .
  3. Differentiate the sine function: .
  4. Differentiate the tangent function: .
Combine these derivatives:
So, the derivative is:

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Extra Insights

To differentiate the function , you’ll want to use the chain rule. Start with the outer function where . The derivative of is . Next, differentiate where . For , utilize the chain rule again with where , and proceed to differentiate into the mix. Carefully apply the derivatives step-by-step to arrive at .
Remember to keep track of your chain rule applications, as it can get a bit tangled. Each function’s derivative contributes to the overall complexity, so a little patience will go a long way! If you find yourself confused, drawing a diagram of each function and its derivative relationships might help clarify things.

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