6x-3y=4 find dy/dx using differentiating implicity
6 dx -3 dy = 0
dy = 2 dx
dy/dx = 3
To find the derivative dy/dx using implicit differentiation, you need to differentiate each term with respect to x and treat y as an implicit function of x. Here's how you can solve for dy/dx step by step:
1. Start with the given equation: 6x - 3y = 4.
2. Differentiate both sides of the equation with respect to x.
d/dx (6x - 3y) = d/dx (4).
3. Apply the power rule for differentiation to differentiate each term with respect to x:
d/dx (6x) - d/dx (3y) = 0.
4. The derivative of 6x with respect to x is simply 6.
Therefore, we have: 6 - d/dx (3y) = 0.
5. Now, we need to differentiate the term -3y with respect to x. Since y is an implicit function of x, we use the chain rule.
6. Apply the chain rule by differentiating y with respect to x: dy/dx.
Therefore, -3 * dy/dx = 0.
7. Rearrange the equation to solve for dy/dx:
dy/dx = 0 / -3.
8. Simplify:
dy/dx = 0.
So, the derivative dy/dx of the equation 6x - 3y = 4 is 0.