(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.