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$\frac{d}{dx}\left(\left(\sqrt{10}-3\right)^{\frac{x+1}{x+3}}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (10^1/2+3)^((x-3)/(x-1))=(10^1/2-3)^((x+1)/(x+3)). Simplifying. Simplifying. Applying the derivative of the exponential function. 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}}.