Final answer to the problem
$\frac{-x\sin\left(x\right)-3\cos\left(x\right)}{x^{4}}$
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Step-by-step Solution
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(cos(x)/(x^3)). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify \left(x^3\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 2. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply -1 times 3.
Final answer to the problem
$\frac{-x\sin\left(x\right)-3\cos\left(x\right)}{x^{4}}$
