Question

Differentiate y = 8x/ 3 − tan(x)

Answer 1

`(dy)/(dx)=(8(xsec^2(x)-tan(x)+3))/((3-tan(x))^2)`

Explanation:

`y=(8x)/(3-tan(x))\\ \\(dy)/(dx)=((3-tan(x))((d)/(dx)8x)-((d)/(dx)(3-tan(x)))(8x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=((3-tan(x))(8)-(-sec^2(x))(8x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=(24-8tan(x)+8xsec^2(x))/((3-tan(x))^2)\\ \\ (dy)/(dx)=(8xsec^2(x)-8tan(x)+24)/((3-tan(x))^2)\\\\ (dy)/(dx)=(8(xsec^2(x)-tan(x)+3))/((3-tan(x))^2)`

Remember to use the Quotient Rule