Showing the properties of differentiating an integralby greswd Tags: differentiating, integral, properties, showing 

#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
P: 20,941





#3
Jan1813, 03:56 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

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 integralI came up with this problem just out of curiosity. Anyway, thanks for the solution HallsofIvy 



#5
Jan1813, 10:57 PM

P: 426




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