Parametric functions differentiation

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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