00:01
In this question, we are asked to find the derivative of the given function and then find an equation of the tangent line at the given point.
00:07
First, let's find the derivative.
00:11
And to do that, we will first rewrite the function in a slightly different form.
00:17
We will rewrite it as 8 divided by x minus 2 to the 1 1ā2, and then 8 multiplied by x minus 2 to the negative 1ā2 power.
00:34
Now we will differentiate the function.
00:37
And to do that, we will use the chain rule.
00:44
By the chain rule, we first need to differentiate x minus 2.
00:48
The derivative of x minus 2 equals to 1.
00:51
So we need to multiply 8 by 1, and then differentiate the negative 1 half's power.
00:57
The derivative of the negative 1 half's power equals to negative 1 or 2, multiplied by x minus 2 to the negative 1 1 1ā2 recall that by the power rule you need to move the exponent in front and then subtract 1 from the exponent.
01:18
That simplifies to negative 4 times x minus 2 to the negative 3 half power...