Question

Tan(y)+xy=20, find the derivative

Answer 1

We need to calculate the derivative for:

$\tan (y)+xy=20$

For that we have to find a way to isolate y' on the left side.

$\begin{gathered} (\tan (y))^{\prime}+(xy)^{\prime}=(20)^{\prime} \\ y^{\prime}\cdot\sec ^2(y)+x^{\prime}\cdot y+x\cdot y^{\prime}=0 \\ y^{\prime}\cdot\sec ^2(y)+x\cdot y^{\prime}=y \\ y^{\prime}\cdot(\sec ^2y+x)=y \\ y^{\prime}=\frac{y}{\sec ^2y+x} \end{gathered}$