## Final Answer

## Step-by-step Solution

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The derivative of a function multiplied by a constant ($2$) is equal to the constant times the derivative of the function

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$2\frac{d}{dx}\left(\ln\left(\sin\left(5x\right)\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of 2ln(sin(5x)). The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of the linear function times a constant, is equal to the constant.