Calculus 1 Questions? Questions #20, #21, and #23

20.)
Find the derivative of the function:
f(t) = (9t + 9)^(2/3)

21.)
Find the derivative of the function:
g(x) = 8tan(7x)

23.)
Find dy/dx by implicit differentiation and evaluate the derivative at the given point:
xy = 8
(-1, -8)
dy/dx = __________ at (-1, -8): y' = __________

Please show all work and 10 points to best answer! Thanks for all answers in advance!

f(t) = (9t + 9)^(2/3)

Chain rule and power rule

f'(t) = (2/3) * (9t + 9)^(-1/3) * (9)
f'(t) = 6 / (9t + 9)^(1/3)



g(x) = 8 * tan(7x)

Chain rule

g'(x) = 8 * 7 * sec(7x)^2
g'(x) = 56 * sec(7x)^2




xy = 8
x * dy + y * dx = 0
x * dy = -y * dx
dy/dx = -y / x

x = -1
y = -8

dy/dx = 8 / (-1) = -8

you better asked the people of Nigeria on this one.