Question

What is the derivative of this function? I want to check my answer

Find `dy/dx` for `ysin(x^2)+e^(xy) = 1`

My answer was `dy/dx = (-2xycos(x^2)-ye^(xy))/(sin(x^2)+xe^(xy))`

I hope I was right. Thanks :)

Answer 1

Yep! That's what I got too.

Explanation:

`ysin(x^2)+e^(xy)=1`

Apply implicit differentiation.

`ycos(x^2)*2x + sin(x^2)*dy/dx +e^(xy)(x*dy/dx+y)=0`

`2xycos(x^2) + sin(x^2)dy/dx + xe^(xy)dy/dx+ye^(xy) =0`

`(sin(x^2)+xe^(xy))dy/dx = -(2xycos(x^2) + ye^(xy))`

`dy/dx = (-2xycos(x^2) - ye^(xy))/(sin(x^2)+xe^(xy))`