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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.
The population of a city is observed as growing exponentially according to the function P(t) = P0 e kt , where the population doubled in the first 50 years. (a) Find k to three
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