Question

Find Dy/Dx In Terms Of X And Y If Ax4−By5=C4. Assume That A,B And C Are Constants.

Answer 1

The derivative of Ax^4 - By^5 = C^4 with respect to x, dy/dx, can be calculated using implicit differentiation and is expressed as 4Ax^3 / (5By^4).

Step-by-step explanation:

To find dy/dx for the equation Ax4 − By5 = C4, where A, B, and C are constants, we utilize implicit differentiation. Applying the derivative to each term with respect to x gives us:

4Ax3 − 5By4(dy/dx) = 0

Now, to solve for dy/dx, we isolate the term by adding 5By4(dy/dx) to both sides and then dividing by 5By4.

5By4(dy/dx) = 4Ax3
dy/dx = 4Ax3 / (5By4)

Therefore, dy/dx in terms of x and y is 4Ax3 / (5By4).