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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\frac{d}{dx}\left(\frac{\left(3x-1\right)^2}{\left(x^2+3\right)^{6}}\right)$
Learn how to solve problems step by step online. Find the derivative of ((3x-1)/((x^2+3)^3))^2. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. 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(\left(x^2+3\right)^{6}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 6 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}.