Question
Honor Student
Posts: 3
Member Since: ‎02-20-2012
Message 1 of 2 (456 Views)

# Can the HP 50g Differentiate with respect to another variable?

I am trying to find out if the HP 50g can do the following:

x = f(Θ) = 10 sin(2Θ)

Find dx/dt.

Solution by hand is uses the chain rule:

dx/dt = dx/dΘ * dΘ/dt

dx/dt = 20 cos(2Θ) dΘ/dt

Then, ultimately, I would like to derive that equation a second time to get a second derivative dx²/d²t.  This will require using the product rule and the chain rule together.

dx²/d²t = [f ' g + f g ' ]

f = 20 cos (2Θ)

g = dΘ/dt

f ' = -40 sin (2Θ) dΘ/dt

g' = dΘ²/d²t

Substituting f, g, f ', g'  back in we get:

dx²/d²t = -40 sin (2Θ) (dΘ/dt)² + 20 cos (2Θ) dΘ²/d²t

Now, I would like to be able to do this on the HP 50g because as you can see it is going to get rather ugly.  This is for an Engineering Dynamics course.

Thanks for your time.

PhD Student
Posts: 725
Member Since: ‎08-10-2010
Message 2 of 2 (439 Views)

# Re: Can the HP 50g Differentiate with respect to another variable?

Hi,

Perhaps the following will be of use to you:

HP-50g The chain rule for partial derivatives

Note: the manual it refers to is the 887 page "HP-50g User's Guide" found here:

HP-50G Manuals

See the "User Guide" list title: HP 50g_users guide_English_E_DCVL5300788.pdf (the 9.54 MB file)

Regards,

Bart

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Note: I do not work for HP, I just like playing with calculators :-)
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