Question

Find the derivative with respect to x of the given combination value of

x √f(x)+g(x), x =3



I know d(√g(x)) = u /( 2√u )

and

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

For this particular problem I tried to use both but I'm can't figure out how the answer ended up with a 15 on the numerator.

Answer 1

\[\sqrt{f(x)+g(x)}\]

u = f(x) + g(x)

du = f'(x) + g'(x)
\[d\sqrt u=\frac{1}{2\sqrt u}du\]\[=\frac{f'+g'}{2\sqrt{f+g}}\]

Answer 2

= (8 + 7) / 2sqrt(1 + 4)

= 15 / 2sqrt(5)

Answer 3

Awesome! That makes this much more easier! Thank you so much!