Question

can anyone help me with this question?
differentiate the implicit equation.
60x =15y + 0.0225*x^2* y

Answer 1

Hey :)

Whenever you're differentiating implicitly, with respect to x, you differentiate the y's as if they were x's, but when you're done, multiply it with dy/dx

Answer 2

For instance, the 60x its derivative is just 60, so that's that for the left-hand side
in 15y, its derivative, is 15 but since it was a y, you multiply it with dy/dx

Answer 3

so for 0.0225*x^2*y, is the derivative (0.0225*x^2*dy/dx+0.0225*2x*y)?

Answer 4

Yeah, actually :D

Answer 5

Oh, Thanks!
there's another part of this question which requires to substitute x=20 & y=50 into the dy/dx & the given answer is 1.875 but somehow i could only get 0.625

Answer 6

hmm? I'm afraid I don't quite get it.

Answer 7

okay, let's try it...
\[\large 60 = 15\frac{dy}{dx}+0.0225x^2\frac{dy}{dx}+0.045xy\]

Answer 8

Now, plug in x=20 and y=50
\[\large 60 = 15\frac{dy}{dx}+0.0225(20)^2\frac{dy}{dx}+0.045(20)(50)\]

Answer 9

\[\large 60 = 15\frac{dy}{dx}+9\frac{dy}{dx}+45\]

Answer 10

Did I miss anything?

Answer 11

\[\large 60-45 = \frac{dy}{dx}(15+9)\]

Answer 12

I'm getting 0.625 too
That's strange...
Maybe you're just too smart? :)

Answer 13

really thanks for your help! I just know that the model answer was incorrect. XP

Answer 14

Haha right