Question

Find the derivative of the function.
f(t) = t^(3/2)log9(sqrt(t + 5))

the 9 is a small number after the log

Answer 1

\[f(t)=t^{3/2}\log_{9}(\sqrt{t+5}) \]

Answer 2

product rule

Answer 3

okiay could you help me with that

Answer 4

the product rule i get but just with this problem im confused

Answer 5

\[f(t)=\frac{1}{2}t^{3/2}\log_{9}(t+5)\]

Answer 6

lets say
y=log(base 9)(t+5)
y=ln(t+5)/ln(9) change of base formula
\[y'=\frac{1}{\ln(9)(t+5)}\]

Answer 7

f(t)=(1/2)t^(3/2)y
f'(t)=(1/2)((3/2)t^(1/2)y+y't^(3/2)

Answer 8

now we just substitue the values back in

Answer 9

ok

Answer 10

\[f'(t)=\frac{1}{2}(\frac{3}{2}t^{\frac{1}{2}}\log_{9}(t+5)+\frac{t^{\frac{3}{2}}}{\ln(9)(t+5)})\]

Answer 11

the person that gave u this problem is a jerk