Given x=12t+42\ and\ y=66t^{2}+143 (i)\frac{dx}{dt}= (ii)\frac{dy}{dt}= (iii)\frac{dy}{dx}=

Painevg

Painevg

Answered question

2021-12-10

Given x=12t+42 and y=66t2+143
(i)dxdt=
(ii)dydt=
(iii)dydx=

Answer & Explanation

Jillian Edgerton

Jillian Edgerton

Beginner2021-12-11Added 34 answers

It should help

Step 1
The derivative is defined as the rate of change of one quantity with respect to another. In order to minimise or maximise a quantity, derivative of that function is calculated and equated to zero in order to calculate critical points. Derivative of any function represents the rate of change of that function. Using the critical points, the maximum or the minimum values of the function can be calculated.
Derivative of any function can be calculated using some basic rules of differentiation and is often represented as  dy  dx  if y has to differentiated with respect to x.  dy  dx  represents the rate of change of y with respect to x.
Step 2
Given,
x=12t+42
First calculating  dx  dt :
x=12t+42
 dx  dt =12xt1−1+0
 dx  dt =12xt0
 dx  dt =12(1)
 dx  dt =12
Also,
x=12t+42
x-42=12t
12t=x-42
t=x12−4212
Now, calculate  dt  dx 
t=x12−4212
 dt  dx =12x1−1−0
 dt  dx =112x0
 dt  dx =112
Step 3
Given,
y=66t2+143
Now calculating  dy  dt 
y=66t2+143
 dy  dt =66⋅2⋅t2−1+0
dydt=132t
Step 4
Now,
 dy  dx = dy  dt x dt  dx 
Using above calculated derivatives:
 dy  dx =132tx112
dydx=11t

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