All parts of this problem refer to the function below. y =...

All parts of this problem refer to the function below. y = (6 + 4x)^{5/x} a) Use logarithmic differentiation to find dy/dx dy/dx = b) Find the slope of the tangent line at x = 1. Slope = c) Find the equation of the tangent line at x = 1. Tangent line: y =

Transcript

00:01 So here in this question, we are given the function that is y is equal to 6 plus 4 of x raised to the power 5 that is divided by x.

00:10 So we have to find out the logarithmic differentiation to find out the value of dy divided by dx in the first part.

00:17 Then after that we have to find out the slope to the tangent at the line that is x is equal to 1 that equation of the tangent.

00:27 So from here we are given this equation.

00:30 So what we have to do is we have to take log on both sides.

00:35 So taking log on both sides, we get the value that is ln of y is equal to ln of 6 plus 4 of x raised to the power 5 that is divided by x.

00:45 So we can write it as that is ln of y is equal to 5 divided by the x of ln of 6 plus 4 of x.

00:52 So we have to find out the value of dy divided by dx from here.

00:56 So taking the differentiation that is d divided by dx of ln of y is equal to d divided by dx of 5 that is divided by x multiplied by the ln of 6 plus 4 of x.

01:08 So 1 divided by y, d of y divided by dx from here is equal to 4 that is divided by, sorry, 5 that is divided by the x multiplied by the 4 that is divided by 6 plus 4 of x plus minus of 5 that is divided by x raised to the power 2 ln of 6 plus 4 of x.

01:34 So this from here is equal to 1 divided by y, dy divided by the dx is equal to 20 that is divided by 20 that is divided by x multiplied by the 6 plus 4 of x minus 5 divided by x raised to the power 2 ln of 6 plus 4 of x.

01:57 So the value of dy divided by the dx from here is equal to y multiplied by the 20 that is divided by the x multiplied by 6 plus 4 of x minus 5 ln of 6 plus 4 of x that is divided by x raised to the power 2.

02:11 So dy divided by dx from here is equals to y and we are having the value of y that is 6 plus 4 of x raised to the power 6 plus 4 of x raised to the power 5 divided by x multiplied by the 20 divided by the x multiplied by the 6 plus 4 of x minus 5 ln of 6 plus 4 of x that is divided by x raised to the power 2.

02:36 So this is the value of dy divided by dx hence the answer to the part a.

02:40 Now we are considering the tangent at the point where x is equals to 1.

02:45 So from here the value of dy divided by the dx at the point that is x is 1 is equals to plugging into the value that is 6 plus 4 is equals to 10 10 raised to the power 5 multiplied by the 20 that is divided by 1 multiplied by the 10 minus 5 of ln of 10 divided by x 1 that is x raised to the power 2...

Question

All parts of this problem refer to the function below. y = (6 + 4x)^{5/x} a) Use logarithmic differentiation to find dy/dx dy/dx = b) Find the slope of the tangent line at x = 1. Slope = c) Find the equation of the tangent line at x = 1. Tangent line: y =

Please give Ace some feedback