use implicit differentiation to find dy/dx for this 8x+y^2=100?

Question

please provide detail & solution

Answer 1

8x+y^2=100

separate the variables x & y:

y^2 = 100 - 8x

y = sqrt(100 - 8x)..........keep this in mind for substitution later on

y^2 = 100 - 8x

differentiate both sides w.r.t. 'x':

2y(dy/dx) = -8

y(dy/dx) = -4

(dy/dx) = (-4/y)

now substitute for 'y' from what we have found out.

dy/dx = (-4) / sqrt(100 - 8x)

this is the answer.

Answer 2

Use implicit differentiation when an equation cannot be easily put into the form of y = f(x).

If you need a REAL easy-to-understand explanation of implicit differentiation so you can ace your next test, try http://web.mit.edu/wwmath/calculus/differentiation/implicit.html

Use implicit differentiation to find dy/dx: 8x + y^2 = 100.

Rearrange equation, expressing y in terms of x.
Equation (1)______y^2 = 100 - 8x.

Take the derivative of y with respect to x:
2y(dy/dx) = 0 - 8

Solve for dy/dx:
dy/dx = -8 / 2y__(Reduce) dy/dx = -4 / y __***Answer in terms of y***

To get the answer in terms of x, solve for y in Equation (1) above:
y^2 = 100 - 8x,
y = √(100 - 8x). Substitute this into the equation, dy/dx = -4 / y
dy/dx = -4 / (√(100 - 8x) ___***Answer in terms of x***

(Keep in mind for real world problems that the square root of a number can be positive or negative...for example, √4 has two answers: +2 and -2. Forgetting this can make bridges collapse.)

Answer 3

Q:- 8x+y^2=100
A:- By differentiating the function w.r.t. x :-
8+2y(dy/dx)=0
=>4+y(dy/dx)=0
=>dy/dx = -4/y

that's the answer.
if u want more detail.
write to me.
i'll explain it to u in more detail.

Answer 4

8x + y^2 = 100

Differentiate.

8 + 2y [dy/dx] = 0

Isolate (dy/dx).

2y[dy/dx] = -8
dy/dx = (-8)/(2y)

Simplify.

dy/dx = -4/y