You are given the following equation. 4x2 + 49y2 = 196

a. Find dy / dx by implicit differentiation.
dy / dx =

b. Solve the equation explicitly for y and differentiate to get dy/dx in terms of x. (Consider only the first and second quadrants for this part.)

dy / dx =

c. Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Step-by-step explanation:

Given the equation  4x²+ 49y² = 196

a) Differentiating implicitly with respect to y, we have;

b)  To solve the equation explicitly for y and differentiate to get dy/dx in terms of x,

First let is make y the subject of the formula from the equation;

If 4x²+ 49y² = 196

49y² = 196 - 4x²

Differentiating y with respect to x using the chain rule;

Let

c) From the solution of the implicit differentiation in (a)

Substituting into the equation to confirm the answer of (b) can be shown as follows

This shows that the answer in a and b are consistent.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

2

step-by-step explanation: