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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
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$\frac{\frac{d}{df}\left(fra\left(cs^2+12\right)\right)\left(s^2-9\right)-fra\left(cs^2+12\right)\frac{d}{df}\left(s^2-9\right)}{\left(s^2-9\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative using the quotient rule (fra(cs^2+12))/(s^2-9). 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 the product -(cs^2+12). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=.