Question

Find the differential of y=sqrt(9+t^2)

Answer 1

y = sqrt(9 + t^2)
= (9 + t^2)^(1/2) putting it into exponential form to use product rule

We could use chain rule, where f(x) = x^(1/2) and g(x) = 9 + t^2
y' = f'(g(x)) * g'(x)
f'(x) = (1/2)x^(-1/2)
= (1/2x^(1/2))
So, we plug in g(x) for x
f'(g(x)) = (1/2(9 + t^2)^(1/2))

g'(x) = 2t

So, f'(g(x)) * g'(x) = 2t * (1/2(9 + t^2)^(1/2))
= t/(9 + t^2)^(1/2)

\[ y' = \frac{t}{\sqrt{9 + t^{2}}} \]

Answer 2

sorry, not 'product rule', i mean 'power rule'.

Answer 3

Thank you AccessDenied! :D

Answer 4

No problem. Glad to help! :)