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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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$\frac{\frac{d}{dx}\left(x^2\left(x-8\right)^3\right)\left(x^2+8\right)^7-x^2\left(x-8\right)^3\frac{d}{dx}\left(\left(x^2+8\right)^7\right)}{\left(\left(x^2+8\right)^7\right)^2}$
Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx((x^2(x-8)^3)/((x^2+8)^7)). 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+8\right)^7\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 7 and n equals 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.