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How do you find #(dy)/(dx)# given #3x+2y=4#?

Answer 1

Samantha Adkison

#(d y)/(d x)=-3/2#

#3x+2y=4" ; "(d y)/(d x)=?#

#"rearrange the equation"#

#2y=-3x+4#

#y=-3/2 x+2#

#(d y)/(d x)=-3/2#

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Answer 2

Samantha Adkison

To find (dy)/(dx) given the equation 3x + 2y = 4, you can follow these steps:

Rewrite the equation in the form y = f(x).
Differentiate both sides of the equation with respect to x.
Solve for (dy)/(dx).

Step 1: Rewrite the equation in the form y = f(x): 3x + 2y = 4 2y = 4 - 3x y = (4 - 3x)/2

Step 2: Differentiate both sides of the equation with respect to x: (d/dx)y = (d/dx)((4 - 3x)/2)

Step 3: Solve for (dy)/(dx): (d/dx)y = (-3/2)

Therefore, (dy)/(dx) = -3/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.