`y = e^sqrt(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 5 - 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 = e^{ax} ; then dy/dx = a*e^(ax)

2) If y = sqrt(x) ; then dy/dx = 1/{sqrt(x)}

3) If y = x^n ; then dy/dx = n*x^(n-1)

Now, y = e^{sqrt(x)}

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

and, f(x) = e^x ............(outer function)

Thus, f(g(x)) = e^{sqrt(x)}.................answer

Now, y = e^{sqrt(x)}

thus, y' = dy/dx = [1/{2*sqrt(x)}]*[e^{sqrt(x)}]

balajia's profile pic

balajia | College Teacher | (Level 1) eNoter

Posted on

The given function is `y=e^(sqrt(x))`

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

Here `f(x)=e^x and g(x)=sqrt(x)`

`dy/dx=e^(sqrt(x))(1/(2sqrt(x)))`

=`(e^(sqrt(x)))/(2sqrt(x))`

We’ve answered 318,947 questions. We can answer yours, too.

Ask a question