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Function of a Function
Suppose y is a function of z,
y = f(z)
and z is a function of x,
z = g(x)
Since, y depends on z, and z in turn depends on x, y is also a function of x.
Thus, y = f(z)
= f[g(x)]
The derivative of y with respect to x can be obtained as:
The above method is often used to get the derivative of some complicated functions.
Water in a canal 30 dm wide and 12 dm deep is flowing with a velocity of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is required for irrigation?
how does it work?
Product Rule: (f g)′ = f ′ g + f g′ As with above the Power Rule, so the Product Rule can be proved either through using the definition of the derivative or this can be proved
?[1,99] x^5+2x^4+x^3+5x^2+6x+2÷x^2+2x
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