# 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(x^{3}))/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(x^{3}))/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(x^{3}))/x.

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