find the slope of the tangent

[Guest]

Find the slope of the tangent to each of the curves at the given point.
y= [(16x^3) square rooted] at (4,32)

 

[stapel]

y= [(16x^3) square rooted]

Does the above mean the following?

. . . . .\(\displaystyle \large{y\,=\,\sqrt{16x^3\,}}\)

Please reply with confirmation or correction.

When you reply, please show the steps that you've tried thus far, starting with finding the derivative.

Thank you.

Eliz.

 

[Guest]

yes,so first I would work inside the square root? So it would be 48x^2? then to get rid of the square root..do I do 48x^2(1/2)?

 

[stapel]

...first I would work inside the square root?

No; the Chain Rules tells you to work from the outside in. So differentiate the one-half power (the square root) first, times the derivative of the root's argument.

Eliz.

 

[Guest]

so 16x^1.5? when u take out the square root..

 

[stapel]

so 16x^1.5?

Where did this come from? Is the "16" not actually inside the square root?

when u take out the square root..

What do you mean by "taking out" the square root? You're supposed to differentiate it.

Please reply with clarification, showing all of your steps. Thank you.

Eliz.