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Jaweria
 2 years ago
Find dy/dx: 4x^2+3xy^26x^2y=y^3.
Jaweria
 2 years ago
Find dy/dx: 4x^2+3xy^26x^2y=y^3.

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abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Using implicit differentiation with respect to x. This means that you take the derivative of everything, even y, but everytime you take the deriviative of y, you multiply it by y'. For instance:\[\frac{ dy }{ dx }(x+y) = 1+\frac{ dy }{ dx } = 1+y'\] then, using your algebra skills, rearrange to find dy/dx

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Remember: \[3xy^2 = 3x \frac{ d }{ dx}y^2+y^2\frac{ d }{ dx }3x\]

Jaweria
 2 years ago
Best ResponseYou've already chosen the best response.0I m little bit confuse here

cwrw238
 2 years ago
Best ResponseYou've already chosen the best response.0what you are doing is treating y as a function of x (which is implied in the expression)

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1Start by taking the derivative as you normally would for the left side of the function. And like @cwrw238 pointed out, you're treating y as a function of x.

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.1If it helps, you can break it down to see it more clearly: \[\frac{ d }{ dx }4x^2 =\] \[\frac{ d }{ dx }3xy^2 = (3x \times \frac{ d }{ dx }y^2)+(y^2\frac{ d }{ dx }3x) = [3x \times 2y \frac{ dy }{ dx }]+[y^2 \times 3]\] \[\frac{ d }{ dx }6x^2y = \] NOW, the right side: \[\frac{ d }{ dx }y^3 = 3y^2\frac{ dy }{ dx } \]
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