If `y=y(x)` and it follows the relation `4x e^(x y)=y+5sin^2x ,` then `y^(prime)(0)` is equal to______

Answer

4

Explanation

We have `4xe^(xy)=y+5sin^(2)x`………….(1)
Putting x=0, in equation (1), we get y=0.
Therefore, (0,0) lies on the curve.
Now, on differentiating equation (1) w.r.t. x, we get
`4e^(xy)+4xe^(xy)(x(dy)/(dx)+y)=(dy)/(dx)+10sinxcosx`
or `y^(')(0)=4`