Question

If ln(4x+y)=2x-3,then dy/dx=

Answer 1

`\ln(4x+y)=2x-3`

Differentiate both sides wrt
`x`:

`(\mathrm d(\ln(4x+y)))/(\mathrm dx)=(\mathrm d(2x-3))/(\mathrm dx)`

By the chain rule, we get

`\frac1{4x+y}(\mathrm d(4x+y))/(\mathrm dx)=2`

`(4+(\mathrm dy)/(\mathrm dx))/(4x+y)=2`

Solve for
`(\mathrm dy)/(\mathrm dx)`:

`4+(\mathrm dy)/(\mathrm dx)=8x+2y`

`\boxed{(\mathrm dy)/(\mathrm dx)=8x+2y-4}`