# Differentials - Check my work

• Nov 22nd 2012, 08:53 AM
friesr
Differentials - Check my work
Not sure I am working these problems correctly. I watched some youtube videos and think I figured it out but would like you to verify my work.

Find the differential of the function. Calculate dy for the given valuse of x and dx.

1) y=sqrt(1+x^2), x=0 dx=0.01

f'(x)=1/2(x^2+1)^(-1/2) (2x) = x/sqrt(x^2+1)
dy=f'(x)dx
dy=x/sqrt(x^2+1)dx
dy=0/sqrt(0^2+1)(0.01)=0

2) y=x^3-6x^2+5x-7, x=-2 dx=0.1

f'(x)=1/4 x^4 - 2x^3 + 5/2 x^2 - 7x

dy = f'(x)dx
dy = (1/4(-2)^2-2(-2)^3 +5/2(-2)^2-7(-2))(0.1)
dy = 4.4

3) cos^2(pit), t=1/3 dt=0.05

f'(t) = -2pi cos(pit)sin(pit)
dy=f'(t)dt
dy = -2pi cos(pi/3)sin(pi/3)(0.05)
dy = -2pi (1/2)(sqrt(3)/2)(0.05)
dy = 1/20(sqrt(3)/4)pi
dy = pi sqrt(3)/80 = 0.068

Thank you for looking,
Rod
• Nov 22nd 2012, 08:59 AM
friesr
Re: Differentials - Check my work
I noticed i did #2 wrong...

f'(x) = 3x^2 - 12x + 5
dy = (3(-2)^2 -12(-2) + 5)(.1)
dy = 4.1
• Nov 22nd 2012, 09:01 AM
SuccessfulSeductress
Re: Differentials - Check my work
Did you try wolfram alpha? Doesn't it do stuff like this?
• Nov 22nd 2012, 09:13 AM
friesr
Re: Differentials - Check my work
Thanks for the tip.

You can enter this type of problem in wolfram?

I am hopeing someone will take the time to let me know if i got the concept correct.
• Nov 22nd 2012, 09:34 AM
hollywood
Re: Differentials - Check my work
On #3, you lost a factor of 2 and a minus sign.

- Hollywood
• Nov 22nd 2012, 09:44 AM
friesr
Re: Differentials - Check my work
Thanks Hollywood!,

Other than the error you noted, what i showed is the correct process for this type of problem?
• Nov 23rd 2012, 12:30 AM
hollywood
Re: Differentials - Check my work