Final Answer
$\frac{2\left(5x+1\right)+5\left(-2x+1\right)}{\left(5x+1\right)^2}+\frac{\frac{\sqrt{2}}{2}}{\sqrt{\left(x-1\right)^{3}}}+\frac{24}{5}\left(3x-1\right)^{3}$
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Step-by-step Solution
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Simplifying
$\frac{d}{dx}\left(\frac{\sqrt{\left(2x-1\right)^2}}{5x+1}+\frac{-\sqrt{2}}{\sqrt{x-1}}+2\left(\frac{\left(3x-1\right)^4}{5}\right)\right)$
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$\frac{d}{dx}\left(\frac{\sqrt{\left(2x-1\right)^2}}{5x+1}+\frac{-\sqrt{2}}{\sqrt{x-1}}+2\left(\frac{\left(3x-1\right)^4}{5}\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(((2x-1)^2^1/2)/(5x+1)+(-2^1/2)/((x-1)^1/2)2((3x-1)^4)/5) using the sum rule. Simplifying. Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (\frac{1}{5}) is equal to the constant times the derivative of the function.
Final Answer
$\frac{2\left(5x+1\right)+5\left(-2x+1\right)}{\left(5x+1\right)^2}+\frac{\frac{\sqrt{2}}{2}}{\sqrt{\left(x-1\right)^{3}}}+\frac{24}{5}\left(3x-1\right)^{3}$