# Calculus

posted by .

arcsinxy = 2/3 arctan4x find dy/dx at the point (1/4, 2)

• Calculus -

using implicit differentiation,

(xy'+y)/√(1+x^2y^2) = 8/3 * 1/(1+16x^2)

a little rearranging of terms yields

y' = 8√(1+x^2y^2) / (3x(1+16x^2)) - y/x

• Calculus -

oops that's 1-x^2y^2 throughout

• Calculus -

when I plug in the ordered pair (.25, 2)I get a zero in the denominator, was I doing that wrong?

• Calculus -

√(1-x^2y^2) = 0, all right, but it's not in the denominator.

So, all you end up with is -y/x = -16

• Calculus -

oops: -2/.25 = -8

• Calculus - final correction -

Rats! I keep being inconsistent in the squaring! √(1-x^2y^2) is not zero.

at (1/4,2)

y' = 8√(1-1/4)/(3*1/4*2) - 2/.25
= (8√6)/3 - 8

judging from my other posts, you'd better double-check this one too!

## Similar Questions

1. ### Pre-calculus

Find the critical point of the function y=-2(x-1)^2-3. Then, determine whether the point represents a maximum, a minimum, or a point of inflection.
2. ### Pre-calculus

Find the critical point of the function y=-2(x-1)^2-3. Then, determine whether the point represents a maximum, a minimum, or a point of inflection.
3. ### Calculus - Damon

Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve …
4. ### calculus

let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the graph of f at the point P = (-2,8) intersects the graph of f again at the point Q. Find the coordinates of point Q. b. Find the coordinates of point R, the inflection …
5. ### AP Calculus

Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y-2x)/(8y-3x) b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P. c) Find the value …
6. ### calculus

optimization find the point on the graph of the function that is closest to the given point f(X)= square root of x point:(8,0)
7. ### Pre-Calculus

Point B is 12 km north of point A. Point C is 9 km from point B on a bearing of 060°. Find the distance from A to C.
8. ### calculus

I needed help with these FRQ in my APCalc course. Any help or walkthrough would be extremely helpful - thanks in advance. Let f be the function given by f(x)=3ln((x^2)+2)-2x with the domain [-2,4]. (a) Find the coordinate of each relative …
9. ### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
10. ### calculus

8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has …

More Similar Questions