Final answer to the problem
$\frac{-\sin\left(\ln\left(x+2\right)\right)}{x+2}$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of cos(ln(x+2)). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). 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}. Multiplying the fraction by -1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Final answer to the problem
$\frac{-\sin\left(\ln\left(x+2\right)\right)}{x+2}$
