Final answer to the problem
$\frac{\left(5x^{4}+16.3923048x^{2}\right)\left(-0.4142136+x\right)-9.8284271-x^5-5.4641016x^3}{\left(-0.4142136+x\right)^2}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\frac{x^5+\left(3.4641016+2\right)x^3+2\sqrt{2}+7}{x-\sqrt{2}+1}\right)$
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$\frac{d}{dx}\left(\frac{x^5+\left(3.4641016+2\right)x^3+2\sqrt{2}+7}{x-\sqrt{2}+1}\right)$
Learn how to solve problems step by step online. Find the derivative of (x^5+(23^1/2+2)x^322^1/2+7)/(x-2^1/2+1). Simplifying. Simplifying. 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 -(9.8284271+x^5+5.4641016x^3).
Final answer to the problem
$\frac{\left(5x^{4}+16.3923048x^{2}\right)\left(-0.4142136+x\right)-9.8284271-x^5-5.4641016x^3}{\left(-0.4142136+x\right)^2}$