Question

differentiate implicity the following equations. show complete solutions

1. e^(2x+3y) =x^2 - In(xy^3)

2. x^2 y^3 = xy+x^3 + y^2 + 5

Answer 1

$1.\ e^{(2x+3y)} =x^2 - In(xy^3)$

Differentiating both sides w.r.t $x$

$e^{(2x+3y)}\{2+3y'\} =2x-\frac{1}{xy^3}.[y^3+2xy^2y']$

$2. x^2 y^3 = xy+x^3 + y^2 + 5$

Differentiating both sides w.r.t $x$

$2xy^3+2x^2y^2y'=y+xy'+3x^2+2yy'$