## Calculus Tutorial

*Parametric functions differentiation*

#### Intro

In general, to find the derivative of a function defined parametrically by the equations x=u(t), y=v(t), we use the following rule

dy/dx=(dy/dt).(dt/dx)=v(t)/u(t)

#### Sample Problem

A curve in the plane is defined parametrically by the equation x=ln(3t-2), y=4t2

find the value of dy/dx at t=1

#### Solution

x=ln(3t-2)

dx/dt=(1/(3t-2)).3

y=4t2

dy/dt=8t

dy/dx=dy/dt.dt/dx

dy/dx=8t.1/(3/(3t-2))

dy/dx=8t.(3t-2)/3

dy/dx (at t=1) =8.1(3.1-2)/3

=8(1)/3

8/3

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