`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/

Textbook Question

Chapter 3, 3.4 - Problem 3 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

2 Answers | Add Yours

hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

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

balajia's profile pic

balajia | College Teacher | (Level 1) eNoter

Posted on

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)`

We’ve answered 318,963 questions. We can answer yours, too.

Ask a question