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Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{\cos\left(x\right)^{4}}{\sin\left(x\right)^2}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (cos(x)^2cos(x)^2)/(sin(x)^2). Simplifying. 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(\sin\left(x\right)^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 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}.