Find the derivative by solving the given implicit equation for y explicitly in terms of x.

Question

Find the derivative  by solving the given implicit equation for y explicitly in terms of x.

Quizplus · Accepted Answer

To find the derivative of the given implicit equation, we need to first solve for y explicitly in terms of x.

11eb12b0_aa05_25c0_b394_3d144ebd756c_TB7866_11

Adding 25x^2 to both sides, we get:

11eb12b0_aa05_25c1_b394_e35161919983_TB7866_11

Taking the square root of both sides, we get:

y = ± √(25x^2 + 1)

Note that we have a ± sign in front of the square root, indicating that there are two possible values of y for each value of x.

Now, we can take the derivative of y with respect to x by using the chain rule:

dy/dx = ± (1/2)(25x^2 + 1)^(-1/2) (50x)

Simplifying, we get:

dy/dx = ± 25x / √(25x^2 + 1)

Therefore, the correct choice is A.

Find the Derivative by Solving the Given Implicit Equation