12 lines
409 B
TeX
12 lines
409 B
TeX
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\begin{align*}
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\left(x^{1/3}-x\right) \cdot \left(x^{2/3}+x^2\right)
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&= x^{1/3} \cdot x^{2/3} + x^{1/3} \cdot x^2 - x\cdot x^{2/3} - x \cdot x^{2} \\
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&= x + x^{7/3} - x^{5/3} - x^3 \\
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\end{align*}
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\begin{align*}
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\frac{d}{dx} \left( x + x^{7/3} - x^{5/3} - x^3 \right)
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&= 1 + \frac{7}{3}x^{4/3} - \frac{5}{3}x^{2/3} - 3x^2 \\
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&= - 3x^2 - \frac{5}{3}x^{2/3} + \frac{7}{3}x^{4/3} + 1
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\end{align*}
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