3.3-bo'lim: Farqlash formulalari
1 – 12 masalalar uchun berilgan funksiyaning hosilasini toping.
- \(f\left( x \right) = 6{x^3} - 9x + 4\) Yechim
- \(y = 2{t^4} - 10{t^2} + 13t\) Yechim
- \(g\left( z \right) = 4{z^7} - 3{z^{ - 7}} + 9z\) Yechim
- \(h\left( y \right) = {y^{ - 4}} - 9{y^{ - 3}} + 8{y^{ - 2}} + 12\) Yechim
- \(y = \sqrt x + 8\,\sqrt[3]{x} - 2\,\sqrt[4]{x}\) Yechim
- \(f\left( x \right) = 10\,\sqrt[5]{{{x^3}}} - \sqrt {{x^7}} + 6\,\sqrt[3]{{{x^8}}} - 3\) Yechim
- \(\displaystyle f\left( t \right) = \frac{4}{t} - \frac{1}{{6{t^3}}} + \frac{8}{{{t^5}}}\) Yechim
- \(\displaystyle R\left( z \right) = \frac{6}{{\sqrt {{z^3}} }} + \frac{1}{{8{z^4}}} - \frac{1}{{3{z^{10}}}}\) Yechim
- \(z = x\left( {3{x^2} - 9} \right)\) Yechim
- \(g\left( y \right) = \left( {y - 4} \right)\left( {2y + {y^2}} \right)\) Yechim
- \(\displaystyle h\left( x \right) = \frac{{4{x^3} - 7x + 8}}{x}\) Yechim
- \(\displaystyle f\left( y \right) = \frac{{{y^5} - 5{y^3} + 2y}}{{{y^3}}}\) Yechim
- \(f\left( x \right) = {x^3} + 9{x^2} - 48x + 2\) funktsiyasi qayerda o'zgarmasligini aniqlang. Yechim
- \(y = 2{z^4} - {z^3} - 3{z^2}\) funktsiyasi qayerda o'zgarmasligini aniqlang. Yechim
- \(x = 4\) da \(\displaystyle g\left( x \right) = \frac{{16}}{x} - 4\sqrt x \) ga teguvchi chiziqni toping. Yechim
- \(x = - 1\) da \(f\left( x \right) = 7{x^4} + 8{x^{ - 6}} + 2x\) ga teguvchi chiziqni toping. Yechim
- Ob'ektning istalgan vaqtda t holati \(s\left( t \right) = 3{t^4} - 40{t^3} + 126{t^2} - 9\) tomonidan beriladi.
- Jismning istalgan vaqtda t tezligini aniqlang.
- Ob'ekt hech qachon harakatni to'xtatadimi?
- Ob'ekt qachon o'ngga, qachon chapga harakatlanadi?
- \(h\left( z \right) = 6 + 40{z^3} - 5{z^4} - 4{z^5}\) funksiyasi qayerda ortib, kamayib borayotganini aniqlang. Yechim
- \(R\left( x \right) = \left( {x + 1} \right){\left( {x - 2} \right)^2}\) funksiyasi qayerda ortib, kamayib borayotganini aniqlang. Yechim
- \(f\left( x \right) = {x^3} - 5{x^2} + x\) ga teguvchi chiziq \(y = 4x + 23\) chizig'iga parallel bo'lgan joyni aniqlang. Yechim