00:01
In this question, we are asked to find d -y over dx and then find an equation of the tangent line at the point 03 to the given implicit curve.
00:15
To do that, we will need to differentiate both sides of this equation.
00:21
And whenever we are differentiating y, we need to multiply the expression by d -y over dx.
00:29
So, by the product rule on the left -hand side, we need to find the derivative.
00:34
Of y squared and multiplied by e to the 2x, and add y squared times the derivative of e to the 2x.
00:42
And on the right -hand side, we're going to get 3 times the derivative of y plus the derivative of x squared.
00:52
The derivative of y squared is 2y, but since we're differentiating y, we need to multiply by dy over dx, plus y squared times the derivative of e to the 2x, and the derivative of e to the 2x equals to 2, e to the 2x.
01:13
On the right -hand side, we are going to get 3.
01:16
The derivative of y equals to 1, but since we are differentiating an expression involving y, we need to multiply this by the y over dx, plus the derivative of x squared, which is 2x...