If g(x) = sin(ln x), what is g'(x)

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that g(x) = sin(ln x). The derivative g'(x) has to be determined.

Use the chain rule

g'(x) = [sin(ln x)]'

=> cos (ln x)*[ln(x)]'

=> cos(ln x)*(1/x)

The required derivative g'(x) = `(cos(ln x))/x`

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the chain rule to find out the derivative of the function. Let's say that we have two functions, u(v(x)) and v(x). You can see that u is the outside function and v is the inside function.

The chain rule is acting in this way: the derivative of the outside function multiplied by the derivative of inside function.

u(v(x)) = u'(v(x))*v'(x)

let v(x) = ln x and u(v(x)) = sin(ln x)

[sin(ln x)]' = sin'(ln x)*(ln x)'

[sin(ln x)]' = [cos(ln x)]*(1/x)

Therefore, the derivative of g(x), using the chain rule is g'(x)=[cos(ln x)]/x.

kareemaths's profile pic

kareemaths | College Teacher | (Level 1) Honors

Posted on

g(x) = sin(lnx)

Sol: we have to differentiate with respect to x.

g'(x) = d/dx sin(lnx)

by using chain rule

g'(x) =  cos(lnx) d/dx lnx

= cos(lnx) . 1/x

g'(x)  =  cos(lnx)/x


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