PURE MATHEMATICS - Differential Calculus

 

The Chain Rule

 

 

The Chain Rule Equation

Rates of Change

 

 

 

The Chain Rule Equation

 

This is a way of differentiating a function of a function.

 

 

 

 

Example #1 Differentiate (3x+3)3

 

 

 

Example #2 Differentiate y=(x2+5x)6

 

 

 

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Rates of change

 

The Chain Rule is a means of connecting the rates of change of dependent variables.

 

 

Example #1

 

If air is blown into a spherical balloon at the rate of 10 cm3 / sec. how quickly will the radius grow?

 

 

 

 

Example #2

 

A spherical raindrop is formed by condensation. In an interval of 10 sec. its volume increases at a constant rate from 0.010mm3 to 0.500mm3.

 

Find the rate at which the surface area of the raindrop is increasing, when its radius is 1.0mm

 

 

 

 

 

 

 

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