Derivatives of Functions in Parametric Forms

Some of the common mistakes that people usually make while using logarithmic differentiation have been mentioned below:

• Not Multiplying by y: After logarithmic differentiation, it is mandatory to multiply by y to solve for dy/dx?
• Incorrectly Applying the Chain Rule: Make sure that you have correctly used the chain rule whenever you are differentiating a logarithmic expression.
• Using Wrong Logarithm: It is always advisable to use the natural logarithm (ln) instead of logarithms with other bases.
• Ignoring Domain Restrictions: Natural logarithm is only defined for the positive real numbers; therefore, y>0 whenever you apply logarithmic differentiation.

We use parametric equations for the following reasons:

• Parametric equations represent all those curves that are otherwise impossible to be represented as a single function. Circles, cycloids, ellipses and spirals are all described using parametric equations.
• These equations can easily describe motion of objects over time.
• Parametric equations help in breaking down complex relationships into simpler components. Rather than dealing with single complex equation, one can describe x and y seperately in terms of t parameter.
• These equations extend to three dimensions easily and naturally, so that one can describe curves and surfaces in 3D space.