Question

Find the derivative of the given function at the indicated point.

Answer 1

We're differentiating implicitly which means we're not going to find an explicit function y(x) before differentiating.

Simply power rule each term and don't forget to chain on the y. Since it's not x, we end up with this extra derivative thing y'.

$\rm 3x^2+2y^2=10$
$\rm 6x+4yy'=0$

Plug in x and y,

$\rm 6(1)+4\sqrt{3.5}~y'=0$

and solve for y',

$\rm y'(x)=\dfrac{-6}{4\sqrt{3.5}}$

Hope that helps.

Answer 2

3x^2 + 2y^2=10

d/d(x)= 6x+4y=0

Substitute x coordinate x=1

6(1)+4y'=0
6=-4y'
6/-4=y'
y'= -3/2

therefore the derivative of the function at x=1 is -1.5 or -3/2