Question
Lse an appropriate method of
ifferentiation determine
ne following
ifferentiation determine
ne following
Ask by Harris Li. in South Africa
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To find the derivative of
, use the chain rule multiple times:
- Differentiate the outer cosine function:
. - Differentiate the square root:
. - Differentiate the sine function:
. - Differentiate the tangent function:
.
Combine these derivatives:
So, the derivative is:
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Like
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.