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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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$\frac{\frac{d}{dx}\left(x\sqrt{x^2+1}\right)\sqrt[3]{\left(x+1\right)^{2}}-x\sqrt{x^2+1}\frac{d}{dx}\left(\sqrt[3]{\left(x+1\right)^{2}}\right)}{\left(\sqrt[3]{\left(x+1\right)^{2}}\right)^2}$
Learn how to solve differential calculus problems step by step online. Find the derivative of d/dx((x(x^2+1)^1/2)/((x+1)^2/3)). 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(\sqrt[3]{\left(x+1\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 \frac{2}{3} and n equals 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1.