(y^2+2)^3=x^4y+e^2 find dy/dx using differentiating implicity
Damon and I have done some of them for you.
Now you try some of the others.
Post your solution so we can see where your difficulty is.
These are rather straightforward questions, and you should not expect us just to do the work for you.
I understand what you guys think I am a soldier on duty and I have to turn these in I am runnning out of time and I need help
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To find dy/dx using implicit differentiation, follow these steps:
1. Take the derivative with respect to x of both sides of the equation. Treat y as a function of x and apply the chain rule whenever necessary.
For the left side, we have: (y^2 + 2)^3
Applying the chain rule, the derivative of this expression is: 3(y^2 + 2)^2 * d/dx(y^2 + 2)
For the right side, we have: x^4y + e^2
To differentiate x^4y, we will treat y as a function of x.
The derivative of x^4y with respect to x is: 4x^3y + x^4 * dy/dx
Since e^2 is a constant with respect to x, its derivative is zero.
2. Simplify the derivative expressions obtained from step 1.
The derivative of y^2 + 2 with respect to x is: 2y * dy/dx
3. Rearrange the derivative expressions to isolate dy/dx.
Now let's collect the terms involving dy/dx and move them to the left side of the equation:
3(y^2 + 2)^2 * d/dx(y^2 + 2) - x^4 * dy/dx = -4x^3y
4. Solve for dy/dx.
To find dy/dx, divide both sides of the equation by the coefficient of dy/dx:
dy/dx = (3(y^2 + 2)^2 * d/dx(y^2 + 2) - x^4 * dy/dx) / (-4x^3y + x^4)
Note: The expression d/dx(y^2 + 2) represents the derivative of y^2 + 2 with respect to x, which can be found by applying the chain rule.
If you have the specific value of y and x, you can substitute those values into the equation above to evaluate dy/dx.