Question

find the derivative of the function:
y = 1/(5x-7)^7

Answer 1

\(\bf y=\cfrac{1}{(5x-7)^7}\implies y=(5x-7)^{-7}\) chain rule it

Answer 2

but dont u need to use the quotient rule also?

Answer 3

sure, you could use the quotient rule as well
longer way, but yes

Answer 4

how did the power 7 became negative?

Answer 5

\[y = \frac{1}{(5x-7)^7}\]
\[y = (5x-7)^{-7}\]
Use chain rule now.
\[\frac{dy}{dx} = \frac{d((5x-7)^{-7})}{dx} = -7(5x-7)^{-8}.5 = -35(5x-7)\]

Answer 6

\(\Large a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\)

Answer 7

\[-35(5x - 7)^{-8}\] would that be the answer?

Answer 8

yeap

Answer 9

thank you, god bless

Answer 10

yw