Question

Find dy/dx at x=0 given y=u−(3/u) and u=(1x+1)^4.
a) dy/dx=17
b) dy/dx=14
c) dy/dx=18
d) dy/dx=16
e) dy/dx=19

Answer 1

\[y=u-\frac{3}{u} \qquad u=(x+1)^4\]\[y=(x+1)^4 -\frac{3}{(x+1)^4}\]

Answer 2

yes, but what is the derivative?

Answer 3

Now simplify the function so you would only have to apply the power rule in solving it: \[y=(x+1)^4 -3(x+1)^{-4}\]

Answer 4

Do you know how to apply the power rule here?

Answer 5

yes

Answer 6

So what would you do?

Answer 7

I get 4(x+1)^3+12(x+1)^-5

Answer 8

That's correct

Answer 9

\[4(x+1)^3 +12(x+1)^{-5} \implies 4(x+1)^3 +\frac{12}{(x+1)^{5}}\]