`y = sin(cot(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 4 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Note:- 1) If y = sinx ; then dy/dx = cosx

2) If y = cotx ; then dy/dx = -cosec(^2)x

Now,

y = sin(cotx)

Let g(x) = cotx..............(inner function)

and f(x) = sinx ...........(outer function)

Thus, f(g(x)) = sin(cotx)...................answer

Now, y =  sin(cotx)

thus, dy/dx = y' = cos(cotx)*[-cosec^(2)x]

or, dy/dx = y' = -[cosec^(2)x]*[cos(cotx)]

balajia's profile pic

balajia | College Teacher | (Level 1) eNoter

Posted on

The given function is `y=sin(cotx)`

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

`f(x)=sinx and g(x)=cotx`

`dy/dx=cos(cotx).(-cosec^2x)`

`=-cos(cotx)cosec^2x`

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