Mar L.

asked • 04/27/22

Find dy/dx when;

Find dy/dx when;

a) y=45-7x-3-18xz-12z1/4+15x1/5

b) 𝑦 = −8x2z-5

Mark M.

Check a) for accuracy.
Report

04/27/22

Luke J.

If i'm understanding this, either 1: z is dependent upon x and part a) needs to be framed as a partial derivative of y w.r.t. x or 2: z is supposed to be just some arbitrary constant meant to evaluated for a single value and not dependent upon the variations of the independent variable x.
Report

04/27/22

Luke J.

Some clarification would be appreciated, or if it's a typo, please post the fix in the comments please
Report

04/27/22

Brenda D.

tutor
Clarity, update, and or correction is needed. Mar L are you trying to do partial derivatives? Where the partial derivative of a function of several variables is its derivative with respect to ONE of those variables, in your case x, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary)? Do you want the derivative with respect to x only?
Report

04/28/22

1 Expert Answer

By:

Philip P. answered • 04/28/22

Tutor
5.0 (478)

Affordable, Experienced, and Patient Algebra Tutor

See tutors like this
See tutors like this

I'll do b) for you, then you can apply the same method to do a):


y = -8x2z-5


Apply the Product Rule:


dy/dx = d(-8x2)/dx·z-5 + (-8x2)·d(z-5)/dx


Apply the chain rule to d(z-5)/dx:


dy/dx = -16xz-5 - 8x2·d(z-5)/dz·dz/dx·


dy/dx = -16xz-5 + 40x2z-6·dz/dx


If z does not depend on x, then dz/dx = 0 and dy/dx = -16xz-5

Upvote • 1 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.