a) Find (dy)/(dx) given i x=ln(2t^2) and y=ln(4+t^2) (3 Marks) ii x^3+3x^2y^3-4xy^2=204 at (5,-1) (3 Marks)

Question

Answer 1

a) i) To find

, we need to use the chain rule. Let's start by finding

and

.Given

, we can differentiate with respect to

to get:

Given

, we can differentiate with respect to

to get:

Now, we can use the chain rule to find

:

ii) To find

at the point

, we need to use implicit differentiation.Given

, we can differentiate both sides with respect to

:

Now, we can substitute the point

into the equation:

Simplifying the equation:

Combining like terms:

Solving for

:

Therefore, the answer is:i)

ii)

at

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