Question

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

Answer 1

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

Differentiate both sides wrt $x$:

$\dfrac{\mathrm d(\ln(4x+y))}{\mathrm dx}=\dfrac{\mathrm d(2x-3)}{\mathrm dx}$

By the chain rule, we get

$\dfrac1{4x+y}\dfrac{\mathrm d(4x+y)}{\mathrm dx}=2$

$\dfrac{4+\frac{\mathrm dy}{\mathrm dx}}{4x+y}=2$

Solve for $\frac{\mathrm dy}{\mathrm dx}$:

$4+\dfrac{\mathrm dy}{\mathrm dx}=8x+2y$

$\boxed{\dfrac{\mathrm dy}{\mathrm dx}=8x+2y-4}$