Final answer to the problem
$\frac{\left(\left(2a+2b-b-a\right)a\left(a^2-b^2\right)+\left(a^2+b^2-ab\right)\left(a^2-b^2+a\left(2a-2b\right)\right)\right)\left(a-b\right)\left(a^3+b^3\right)+\left(-a^2-b^2+ab\right)a\left(a^2-b^2\right)\left(a-b\right)\left(3a^{2}+3b^{2}\right)}{\left(a-b\right)^2\left(a^3+b^3\right)^2}$
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Step-by-step Solution
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1
Combine $\frac{1}{b}+\frac{-1}{a}$ in a single fraction
$\frac{d}{da}\left(\frac{\frac{\frac{a^2+b^2}{b}-a}{\frac{-1+\frac{a}{b}}{a}}\left(a^2-b^2\right)}{a^3+b^3}\right)$
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$\frac{d}{da}\left(\frac{\frac{\frac{a^2+b^2}{b}-a}{\frac{-1+\frac{a}{b}}{a}}\left(a^2-b^2\right)}{a^3+b^3}\right)$
Learn how to solve problems step by step online. Find the derivative of b=(((a^2+b^2)/b-a)/(1/b+-1/a)(a^2-b^2))/(a^3+b^3). Combine \frac{1}{b}+\frac{-1}{a} in a single fraction. Combine -1+\frac{a}{b} in a single fraction. Combine \frac{a^2+b^2}{b}-a in a single fraction. Simplify the fraction \frac{\frac{a^2+b^2-ab}{b}}{\frac{\frac{a-b}{b}}{a}}.
Final answer to the problem
$\frac{\left(\left(2a+2b-b-a\right)a\left(a^2-b^2\right)+\left(a^2+b^2-ab\right)\left(a^2-b^2+a\left(2a-2b\right)\right)\right)\left(a-b\right)\left(a^3+b^3\right)+\left(-a^2-b^2+ab\right)a\left(a^2-b^2\right)\left(a-b\right)\left(3a^{2}+3b^{2}\right)}{\left(a-b\right)^2\left(a^3+b^3\right)^2}$