00:01
So, dy by dx, to find dy by dx, the equation given to us is y cube cross 3x square plus n xy square is equal to e raised to x plus 2y, using the implicit differentiation.
00:32
So, we will just solve y cube cross of 3x square and n of xy raised to 2 is equal to e raised to x plus 2y.
00:53
So, differentiate both the side of the equation with respect to x, use the chain rule, product chain rule, product rule and differentiation of n of u.
01:03
So, therefore, we will get d by dx is equal to y cube, y cube cross of 3x square plus d by dx in xy square is equal to d by dx e raised to x plus 2y.
01:32
So, therefore, d by dx in x raised to xy square is equal to 1 upon xy square, xy square dy by dx plus 2y.
01:54
On the right side, the derivative e raised to x plus 2y with respect to x is simply e raised to 2y times the derivative of the exponent, which is 1 upon 2 plus d, 1 plus 2 dy by dx...