3.6-bo'lim: Ko'rsatkichli va logarifm funksiyalarning hosilalari

1-6-masalalar uchun berilgan funksiyani farqlang.

1. \(f\left( x \right) = 2{{\bf{e}}^x} - {8^x}\) Yechim
2. \(g\left( t \right) = 4{\log _3}\left( t \right) - \ln \left( t \right)\) Yechim
3. \(R\left( w \right) = {3^w}\log \left( w \right)\) Yechim
4. \(y = {z^5} - {{\bf{e}}^z}\ln \left( z \right)\) Yechim
5. \(\displaystyle h\left( y \right) = \frac{y}{{1 - {{\bf{e}}^y}}}\) Yechim
6. \(\displaystyle f\left( t \right) = \frac{{1 + 5t}}{{\ln \left( t \right)}}\) Yechim
7. \(x = 0\) da \(f\left( x \right) = {7^x} + 4{{\bf{e}}^x}\) ga teguvchi chiziqni toping. Yechim
8. \(x = 2\) da \(f\left( x \right) = \ln \left( x \right){\log _2}\left( x \right)\) ga teguvchi chiziqni toping. Yechim
9. Quyidagi nuqtalarda \(\displaystyle V\left( t \right) = \frac{t}{{{{\bf{e}}^t}}}\) ortib yoki kamayib borayotganini aniqlang.
   1. \(t = - 4\)
   2. \(t = 0\)
   3. \(t = 10\)
   Yechim
10. Quyidagi nuqtalarda \(G\left( z \right) = \left( {z - 6} \right)\ln \left( z \right)\) ortib yoki kamayib borayotganini aniqlang.
    1. \(z = 1\)
    2. \(z = 5\)
    3. \(z = 20\)
    Yechim