AN: Find \( \frac{\partial w}{\partial u} \) and \( \frac{\partial w}{\partial v} \) and cheak the result by substitution and difformatiat where: \( w=x y, x=e^{u} \cos v, y=e^{u} \sin v \)

\( \int 9 ^ { x ^ { k } + r _ { x } } . \)

Xosmas integrallarni hisoblang yoki uzoqlashuvchi ekanini aniqlang \[ \int_{e^{2}}^{\infty} \frac{d x}{x \ln \ln x} \]

A car's velocity is given by the function \( v(t) = 5t^2 + 3 \). Calculate the distance traveled by the car from time \( t = 0 \) to \( t = 4 \).

5. Найдите общее решение дифференциальног̈ уравнения \( y^{m}=x \)

Berilgan qatorlarni absolyut va shartli yaqinlashishga tekshiring. \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+1) \ln (n+1)} \]