Final Answer
Step-by-step Solution
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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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$\frac{\frac{d}{dm}\left(12m^2+19m^4-11m^3+3m+30m^5+1\right)\left(4m^2+5m^3-2m+1\right)-\left(12m^2+19m^4-11m^3+3m+30m^5+1\right)\frac{d}{dm}\left(4m^2+5m^3-2m+1\right)}{\left(4m^2+5m^3-2m+1\right)^2}$
Learn how to solve problems step by step online. Find the derivative of (12m^2+19m^4-11m^33m30m^5+1)/(4m^2+5m^3-2m+1). 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 -(12m^2+19m^4-11m^3+3m+30m^5+1). Simplify the product -(19m^4-11m^3+3m+30m^5+1). Simplify the product -(-11m^3+3m+30m^5+1).