1. (3x² - 1/x³) ' = (3x²) ' - (1/x³) ' = 6x - (x⁻³)' = 6x + 3x⁻⁴ = 6x + 3/x⁴2. ((x/3 + 7)⁶) ' = 6(x/3 + 7)⁵ · (x/3 + 7)' = 6(x/3 + 7)⁵ · 1/3 = 2(x/3 +7)⁵3. (eˣ·cosx) ' = (eˣ)' · cosx + eˣ · (cosx)' = eˣ · cosx + eˣ · (- sinx) = eˣ(cosx - sinx)4. (2ˣ / sinx) ' =
'sinx - 2^{x}(sinx)' }{ sin^{2}x } = \frac{ 2^{x}ln2 sinx - 2^{x}cosx }{ sin^{2}x } )
5. (2x³ - 1/x²)' = (2x³) ' - (x⁻²)' = 6x² + 2x⁻³ = 6x² + 2/x³6. ((x/7 + 13)⁸) ' = 8(x/7 + 13)⁷ · (x/7 + 13)' = 8(x/7 + 13)⁷ · 1/7 = 8/7 (x/7 + 13)⁷7. (eˣsinx) ' = (eˣ) ' sinx + eˣ (sinx) ' = eˣ sinx + eˣ cosx8. (3ˣ / cosx) ' =