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)=(y)/(\sec ^2y+x) \end{gathered}`