3.4-bo'lim : Mahsulot va miqdor qoidasi
1-7-masalalar uchun berilgan funksiyaning hosilasini topish uchun mahsulot qoidasi yoki qism qoidasidan foydalaning.
- \(h\left( z \right) = \left( {2 - \sqrt z } \right)\left( {3 + 8\,\,\sqrt[3]{{{z^2}}}} \right)\)
- \(\displaystyle f\left( x \right) = \left( {x - \frac{2}{x}} \right)\left( {7 - 2{x^3}} \right)\)
- \(y = \left( {{x^2} - 5x + 1} \right)\left( {12 + 2x - {x^3}} \right)\)
- \(\displaystyle g\left( x \right) = \frac{{\sqrt[3]{x}}}{{1 + {x^2}}}\)
- \(\displaystyle Z\left( y \right) = \frac{{4y - {y^2}}}{{6 - y}}\)
- \(\displaystyle V\left( t \right) = \frac{{1 - 10t + {t^2}}}{{5t + 2{t^3}}}\)
- \(\displaystyle f\left( w \right) = \frac{{\left( {1 - 4w} \right)\left( {2 + w} \right)}}{{3 + 9w}}\)
8-12-masalalar uchun \(f\left( { - 3} \right) = 12\), \(f'\left( { - 3} \right) = 9\), \(g\left( { - 3} \right) = - 4\), \(g'\left( { - 3} \right) = 7\), \(h\left( { - 3} \right) = - 2\) va \(h'\left( { - 3} \right) = 5\) ko'rsatilgan lotin qiymatini aniqlash faktidan foydalaning.
- \({\left( {f\,g} \right)^\prime }\left( { - 3} \right)\)
- \({\left( {\frac{h}{g}} \right)^\prime }\left( { - 3} \right)\)
- \(\displaystyle {\left( {\frac{{f\,g}}{h}} \right)^\prime }\left( { - 3} \right)\)
- Agar \(y = \left[ {x - f\left( x \right)} \right]h\left( x \right)\) \(\displaystyle {\left. {\frac{{dy}}{{dx}}} \right|_{x = - 3}}\)ni aniqlang.
- Agar \(\displaystyle y = \frac{{1 - g\left( x \right)h\left( x \right)}}{{x + f\left( x \right)}}\) \(\displaystyle {\left. {\frac{{dy}}{{dx}}} \right|_{x = - 3}}\)ni aniqlang.
- \(x = - 2\) da \(f\left( x \right) = \left( {8 - {x^2}} \right)\left( {1 + x + {x^2}} \right)\) ga teguvchi chiziq tenglamasini toping.
- \(x = 1\) da \(\displaystyle f\left( x \right) = \frac{{4 - {x^3}}}{{x + 2{x^2}}}\) ga teguvchi chiziq tenglamasini toping.
- \(\displaystyle g\left( z \right) = \frac{{2 - z}}{{12 + {z^2}}}\) qayerda ortib, kamayib borayotganini aniqlang.
- \(R\left( x \right) = \left( {3 - x} \right)\left( {1 - 2x + {x^2}} \right)\) qayerda ortib, kamayib borayotganini aniqlang.
- \(\displaystyle h\left( t \right) = \frac{{7t - {t^2}}}{{1 + 2{t^2}}}\) qayerda ortib, kamayib borayotganini aniqlang.
- \(\displaystyle f\left( x \right) = \frac{{1 + x}}{{1 - x}}\) qayerda ortib, kamayib borayotganini aniqlang.
- To'rt funktsiya uchun mahsulot qoidasi formulasini chiqaring. \[{\left( {f\,g\,h\,w} \right)^\prime } = f'\,g\,h\,w + f\,g'\,h\,w + f\,g\,h'\,w + f\,g\,h\,w'\]