00:01
In this question, we are asked to find an equation of the tangent line to the graph of the given curve at the point 1 -1.
00:07
And the equation of the tangent line is y -minus y -not equals to y -prime of x -not -y -not times x -minus x -0, where x -not and y -not are the coordinates of the given point.
00:28
So the equation could be written as y -minus 1 equals to y -prime of 1 -1 times x -minus 1.
00:37
Now we need to find y -prime.
00:39
To find y prime, we will differentiate both sides of the given equation, assuming that y is a function which depends on x, y equals to y of x.
00:56
And this means that whenever we differentiate an expression involving y, we need to multiply it additionally by y prime.
01:05
The derivative of x cube equals to 3x squared, because x is the independent variable and everything as usual.
01:13
The derivative of y cube equals to 3y squared and since y depends on x we need to multiply it by y prime.
01:23
On the right hand side we will use the product rule...