Differentiate the function. f(x) = sin(3 ln(x))

The chain rule is applied by differentiating a function from outside functions first, to the inside functions.

Answer: The differential of the  function. f(x) = sin(3 ln(x)) is given as  3cos (ln(x³))/x.

Go through the explanation to understand better.

Explanation:

We can make use of the chain rule for differentiation.

Chain rule states that d/dx [f(g(x))] is f'(g(x))g'(x) where, f(x) = sin(x) and g(x) = 3ln(x)

f'(g(x)) = cos(3 ln(x))

g'(x) = d/dx [3lnx] = 3/x

⇒ d/dx [f(g(x))] =  f'(g(x))g'(x) = cos(3 ln(x))× 3/x

On simplifying 3lnx by moving 3 inside, we get:

f'(g(x)) = 3cos (ln(x³))/x

For further calculations, we can make use of the derivatives calculator.

Thus the differential of the  function. f(x) = sin(3 ln(x)) is given as  3cos (ln(x³))/x.