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Is this assumption correct? (V.simple Calculus) watch

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1. Just a very quick question,

Is: d(y + z)/dt = dy/dt + dz/dt where y and z are both functions of t?

Am trying to tackle some circuit theory problems and have had a mental block!

Thanks
2. yes... example...

y=2(t^2) so dy/dt = 4t
z=3t+2 so dz/dt = 3

dy/dt + dz/dt = 4t+3

y+z = 2(t^2) + 3t + 2

let y+z = f(x)

f(x) = 2(t^2) + 3t + 2
f'(x) = 4t+3
3. A more general proof:

d(y + z)/dt = k
d(y + z) = k dt
y + z = kt + c [1]

d(y + z)/dt = k
dy/dt + dz/dt = k
dy + dz = k dt
y + z = kt + c [2]

[1] = [2]

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Updated: January 1, 2005
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