# `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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Expert Answers

hkj1385 | Certified Educator

*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**

Student Comments

balajia | Student

The given function is `y=tan(pix)`

This is in the form `y=f(g(x))`

Here `f(x)=tanx` and `g(x)=pix`

`dy/dx=sec^2(pix).pi`

`=pisec^2(pix)`