00:01
We are wanting to write the equation for the line that is tangent to y equals f of x equals 3x squared over 5x squared plus 7x at the x value of 1.
00:13
Well, to write the equation for a tangent line, the first thing we need to determine is the slope of that tangent line.
00:20
Slope is going to come from the derivative.
00:23
The derivative of our function will fit the quotient rule.
00:28
Now, before i do use the quotient rule, since there is a common firm, let's go ahead and reduce that out.
00:34
So that's 3x over 5x plus 7.
00:38
Using the quotient rule, we have 5x plus 7 times the derivative of the top 3, minus 3x times the derivative of the bottom, 5, all over our denominator squared.
00:55
And we can simplify that down.
00:58
That would be 15x plus 7, which will be plus 21, 3 times 7.
01:08
Minus 15x all over 5x plus 7 squared...