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Showing the properties of differentiating an integral 
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#1
Jan1813, 02:11 PM

P: 147

How do we show that
[tex]\frac{d}{dt}\left[\int\!y\,\mathrm{d} x\right] = y\,\frac{dx}{dt}[/tex] 


#2
Jan1813, 03:33 PM

Mentor
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#3
Jan1813, 03:56 PM

Math
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Thanks
PF Gold
P: 39,353

Of course, then [tex]F(x)= \int y dt[/tex] is the function such that dF/dx= y. Given that, we have that [itex]d/dt(\int y dx)= dF/dt= (dF/dx)(dx/dt)= y(x)(dx/dt)[/itex] by the chain rule. 


#4
Jan1813, 04:07 PM

P: 147

Showing the properties of differentiating an integral
I came up with this problem just out of curiosity. Anyway, thanks for the solution HallsofIvy 


#5
Jan1813, 10:57 PM

P: 445




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