3.3-bo'lim : Farqlash formulalari
1 – 20 masalalar uchun berilgan funksiyaning hosilasini toping.
- \(g\left( x \right) = 8 - 4{x^3} + 2{x^8}\)
- \(f\left( z \right) = {z^{10}} - 7{z^5} + 2{z^3} - {z^2}\)
- \(y = 8{x^4} - 10{x^3} - 9x + 4\)
- \(f\left( x \right) = 3{x^{ - 4}} + {x^4} - 3x\)
- \(R\left( t \right) = 9{t^{10}} + 8{t^{ - 10}} + 12\)
- \(h\left( y \right) = 3{y^{ - 6}} - 8{y^{ - 3}} + 9{y^{ - 1}}\)
- \(g\left( t \right) = {t^{ - 7}} + 2{t^{ - 3}} - 6{t^{ - 2}} + 8{t^4} - 1\)
- \(z = \sqrt[6]{x} - 7\,\sqrt[4]{x} + 3\sqrt x \)
- \(f\left( x \right) = 7\,\sqrt[9]{{{x^4}}} - 2\,\sqrt[2]{{{x^7}}} + \sqrt[3]{{{x^4}}}\)
- \(\displaystyle h\left( y \right) = 6\sqrt y + \sqrt[6]{{{y^5}}} + \frac{7}{{\sqrt[9]{{{y^2}}}}}\)
- \(\displaystyle g\left( z \right) = \frac{4}{{{z^2}}} + \frac{1}{{7{z^5}}} - \frac{1}{{2z}}\)
- \(\displaystyle y = \frac{2}{{3{t^9}}} + \frac{1}{{7{t^3}}} - 9{t^2} - \sqrt {{t^3}} \)
- \(\displaystyle W\left( x \right) = {x^3} - \frac{1}{{{x^6}}} + \frac{1}{{\sqrt[5]{{{x^2}}}}}\)
- \(g\left( w \right) = \left( {w - 5} \right)\left( {{w^2} + 1} \right)\)
- \(h\left( x \right) = \sqrt x \left( {1 - 9{x^3}} \right)\)
- \(f\left( t \right) = {\left( {3 - 2{t^3}} \right)^2}\)
- \(g\left( x \right) = \left( {1 + 2x} \right)\left( {2 - x + {x^2}} \right)\)
- \(\displaystyle y = \frac{{4 - 8x + 2{x^2}}}{x}\)
- \(\displaystyle Y\left( t \right) = \frac{{{t^4} - 2{t^2} + 7t}}{{{t^3}}}\)
- \(\displaystyle S\left( w \right) = \frac{{{w^2}\left( {2 - w} \right) + {w^5}}}{{3w}}\)
21-26-muammolar uchun funktsiya qayerda o'zgarmasligini aniqlang.
- \(f\left( x \right) = 2{x^3} - 9{x^2} - 108x + 14\)
- \(u\left( t \right) = 45 + 300{t^2} + 20{t^3} - 3{t^4}\)
- \(Q\left( t \right) = {t^3} - 9{t^2} + t - 10\)
- \(h\left( w \right) = 2{w^3} + 3{w^2} + 4w + 5\)
- \(g\left( x \right) = 9 + 8{x^2} + 3{x^3} - {x^4}\)
- \(G\left( z \right) = {z^2}{\left( {z - 1} \right)^2}\)
- \(x = - 1\) da \(f\left( x \right) = 3{x^5} - 4{x^2} + 9x - 12\) ga teginish chizig'ini toping.
- \(x = 2\) da \(\displaystyle g\left( x \right) = \frac{{{x^2} + 1}}{x}\) ga teguvchi chiziqni toping.
- \(x = 16\) da \(h\left( x \right) = 2\sqrt x - 8\,\sqrt[4]{x}\) ga teginish chizig'ini toping.
- Ob'ektning istalgan vaqtda t holati \(s\left( t \right) = 3{t^4} - 44{t^3} + 108{t^2} + 20\) tomonidan beriladi.
- Jismning istalgan vaqtda t tezligini aniqlang.
- Ob'ektning pozitsiyasi hech qachon o'zgarishni to'xtatadimi?
- Ob'ekt qachon o'ngga, qachon chapga harakatlanadi?
- Ob'ektning istalgan vaqtda t holati \(s\left( t \right) = 1 - 150{t^3} + 45{t^4} - 2{t^5}\) tomonidan beriladi.
- Jismning istalgan vaqtda t tezligini aniqlang.
- Ob'ektning pozitsiyasi hech qachon o'zgarishni to'xtatadimi?
- Ob'ekt qachon o'ngga, qachon chapga harakatlanadi?
- \(f\left( x \right) = 4{x^3} - 18{x^2} - 336x + 27\) funksiyasi qayerda ortib, kamayib borayotganini aniqlang.
- \(g\left( w \right) = {w^4} + 2{w^3} - 15{w^2} - 9\) funksiyasi qayerda ortib, kamayib borayotganini aniqlang.
- \(V\left( t \right) = {t^3} - 24{t^2} + 192t - 50\) funksiyasi qayerda ortib, kamayib borayotganini aniqlang.
- \(f\left( x \right) = 7 + 10{x^3} - 5{x^4} - 2{x^5}\) ortib borayotgan \(\left[ { - 6,4} \right]\) intervalining foizini aniqlang.
- \(f\left( x \right) = 3{x^4} - 8{x^3} - 144{x^2}\) kamayayotgan \(\left[ { - 5,2} \right]\) oraliq foizini aniqlang.
- \(\left[ { - 1,1} \right]\) oralig'ida \(h\left( x \right) = 3 - x + {x^2} + 2{x^3}\) ko'proq ko'payadimi yoki kamayadimi?
- \(f\left( x \right) = 12{x^2} - 9x + 3\) ga teguvchi chiziq \(y = 1 - 7x\) chizig'iga parallel bo'lgan joyni aniqlang.
- \(f\left( x \right) = 8 + 4x + {x^2} - 2{x^3}\) ga teguvchi chiziq \(\displaystyle y = - \frac{1}{4}x + \frac{8}{3}\) chizig‘iga perpendikulyar bo‘lgan joyni aniqlang.
- \(f\left( x \right) = \sqrt[3]{x} - 8x\) ga teguvchi chiziq \(y = 2x - 11\) chizig‘iga perpendikulyar bo‘lgan joyni aniqlang.
- \(\displaystyle f\left( x \right) = \frac{{13x}}{9} + \frac{1}{x}\) ga teguvchi chiziq \(y = x\) chizig'iga parallel bo'lgan joyni aniqlang.