Question

Find the differential of each function. a. y = s / ( 1 + 5s ) b. y = e^-u Cos U

Answer 1

Answer:

To find the differentials, we must derivate:

a) y = s/(1 + 5s)

remember that when we have a function:

f(x) = h(x)*g(x)

we have that the differentiation rule is:

f'(x) = h'(x)*g(x) + h(x)*g'(x)

using this rule, we have:

$dy/ds = \frac{1}{1 + 5s} - 5*\frac{s}{(1+5s)^2}$

Then te differential is:

$dy = (\frac{1}{1 + 5s} - 5*\frac{s}{(1+5s)^2})ds$

b) now the function is:

y = e^(-u)*cos(u)

We use the same rule as before for the derivation:

$dy/du = -1*e^{-u}*cos(u) + (e^{-u}*(-sin(u))$

Then we have:

$dy = (-e^{-u}*cos(u) - e^{-u}*sin(u))du = -e^{-u}*(cos(u) + sin(u))du$