What is the second derivative value for the function g(x)=sin (9x)?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the function g(x) = sin 9x.

We have to find the second derivative of g(x). We use the chain rule here.

g(x) = sin 9x

=> g'(x) = 9 cos 9x

=> g''(x) = -81 sin 9x

The required second derivative is -81 sin 9x

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll differentiate the given functin with respect to x, using the chain rule.

g'(x) = [sin (9x)]'

g'(x) = [cos (9x)]*(9x)'

g'(x) = 9*cos (9x)

Now, we'll differentiate the expression of g'(x), with respect to x:

g"(x) = [9*cos (9x)]'

g"(x) = 9*(-sin (9x))*(9x)'

g"(x) = -81sin (9x)

The value of the second derivative of the given function is g"(x) = -81sin (9x).

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