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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.
Differentiate y = x x Solution : We've illustrated two functions similar to this at this point. d ( x n ) /dx = nx n -1 d (a x ) /dx= a
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