Question

need help with a derivative :)

Answer 1

trying to find the derivative of \[y=\sqrt(9-\frac{ 9 }{ 16 }x^2)\]

Answer 2

so I did the power rule and got \[\frac{ 1 }{ 2 }(9-\frac{ 9 }{ 16 }x^2)^{-1/2}\frac{ -18x }{ 16 }\]

Answer 3

is that right? I did the chain rule and power rule

Answer 4

You got a point there. You have to use first the chain rule and then the power rule.
Can you identify the internal and the external functions?

Answer 5

Remember that \[\frac{ d }{ dx } u(v(x)) = u'(v)*v'(x)\]

Answer 6

Yeah, I dropped down the 1/2 power, subtracted one, then did the derivative of the inner function

Answer 7

It is right. Though you could multiply 1/2 * -18/16 ;)

Answer 8

okay thanks :) I was just curious how the book got it simplified into their answer of \[\frac{ -3x }{ 4\sqrt(16-x^2) }\]

Answer 9

oh wait, I see it now. Thanks for the help :)

Answer 10

You're welcome.