`y = tan(pi x)` Write the composite function in the form f(g(x)). Identify the inner function u = g(x) and the outer function y =f(u). Then find the derivative dy/

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Note:- 1) If y = ax ; then dy/dx = a ; where a = constant

2) If y = tanx ; then dy/dx = sec^(2)x

Now, y = tan(pi*x)

Let  g(x) = pi*x.............(inner function)

and, f(x) = tanx..........(outer function)

Thus, f(g(x)) = tan(pi*x).............answer

Now, y = tan(pi*x)

thus, dy/dx = y' = sec^(2)(pi*x) *[pi]

or, dy/dx = y' = pi*sec^(2)(pi*x)  .............answer

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