(a) The value of
is
.
(b) The value of
is
.
Further explanation:
Given that
and
are both differentiable functions of
.
The function is as follows:

Derivatives of parametric functions:
The relationship between variable
and variable
in the form
and
is called as parametric form with
as a parameter.
The derivative of the parametric form is given as follows:
The above equation is neither explicit nor implicit, therefore a third variable is used.
Part (a):
It is given that
and
.
To find the value of
first find the value of
that is shown below:
The value of
is calculated as follows:

Now, substitute the value of
and
in above equation as shown below:
Therefore, the required value of
is
.
Part (b):
It is given that
and
.
To find the value of
first find the value of
that is shown below:

The value of
is calculated as follows:

Now, substitute the value of
and
in above equation as shown below:

Therefore, the required value of
is
.
Learn more:
1. A problem on trigonometric ratio brainly.com/question/9880052
2. A problem on function brainly.com/question/3412497
Answer details:
Grade: Senior school
Subject: Mathematics
Chapter: Derivatives
Keywords: dy/dt, dx/dt, y=rootx, derivatives, parametric form, implicit, explicit, function, differentiable, x, y, t, x=16, x=64, dy/dx, dx/dy, differentiation.