Solution assignment 04 Implicit differentiation

Calculate $y'$ if:

$x\ln(y)-4=0$

Implicit differentiation in combination with the product rule gives:

$1.\ln(y)+x\cdot\displaystyle\frac{1}{y}\cdot{y'}=0$

thus:

$y'=-\displaystyle\frac{y\ln(y)}{x}$

Also in this case implicit differentiation is not necessary. We can rewrite the original expression as:

$y=e^{\frac{4}{x}}$

and thus:

$y'=e^{\frac{4}{x}}\cdot-\displaystyle\frac{4}{x^2}$

After some calculations we get the same result. Verify.