Home >> PURE MATHS, Differential Calculus, the chain rule

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 0.500mm^3.

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

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