00:01
In this question, we are asked to find an equation of the tangent line to the given curve at the given point.
00:06
And the general formula for the tangent line is y minus y0 equals to y prime of x0 y0, multiplied by x minus x0, where x0 and y0 are the coordinates of the given point.
00:25
So we're going to rewrite it as y minus 1 equals to y prime of 4 1 times x minus 4.
00:33
Now we just need to find y prime.
00:37
And to find y prime, we need to differentiate the equation.
00:50
And when differentiating this, we will differentiate this equation implicitly, meaning that we will assume that y depends on x.
00:58
And x is the independent variable.
01:01
This means that we differentiate x as usual.
01:05
And when differentiating y, we need to additionally multiply the expression by y prime.
01:10
We need to differentiate xy and subtract the derivative of 3y squared, and that's going to be equal to 0 because the derivative of 1 is 0, because 1 is a constant.
01:28
To differentiate xy, we'll use the product rule...