# calculus

posted by .

Point P(a,b) is on the curve
square root of x + square root of y =1.

Show that the slope of the tangent at P is : - square root of (b/a).

• calculus -

√x + √y = 1 or
x^(1/2) + y^(1/2) = 1
differentiate implicitly
(1/2)x^(-1/2) + (1/2)y^(-1/2)dy/dx = 0
dy/dx = -x^(-1/2)/y^(-1/2)
= - y^(1/2)/x^(1/2)
= - √y/√x
= - √(y/x)

so at the point (a,b)
dy/dx = - √(b/a)

• implicit differentiation -

Given
√x + √y = 1
Apply implicit differentiation:
1/(2√x) + 1/(2√y)*(dy/dx) = 0
Transposing and solving for dy/dx:

dy/dx = -√(y/x)

• calculus -

Find dy/dx by implicit differentiation
(1-2xy^3)^5=x+4y

## Similar Questions

1. ### calculus

Point P(a,b) is on the curve square root of x + square root of y =1. Show that the slope of the tangent at P is : - square root of (b/a).
2. ### Algebra

Rationalize each expression by building perfect nth root factors for each denominator. Assume all variables represent positive quantities. I don’t understand how to compute these. Also I don’t have the square root sign so I typed …
3. ### Math simplifying mixed radicals

Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root: 2 square root 48 3 square root 81 6 square root 12 …
4. ### Math simplifying mixed radicals

Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are supposed …
5. ### Math ~CHECK MY ANSWER~

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers?
6. ### college pre-calculus

simplify: square root (4/3)-square root (3/4) A. 2-sqaure root(3)/2 square root (3) B. square root (7/12) C. square root (3)/6 D. 2/square root (3) which answer?
7. ### Calculus

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum?
8. ### math

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers?
9. ### math

Four students work to find an estimate for square root 54. Who is closest to finding the true estimate?
10. ### Math

Four students work to find an estimate for square root 27. Who is closest to finding the true estimate?

More Similar Questions