SOLUTION: (a) Find dy/dx for {{{ xy^4+sqrt(2x+3y)= 6 }}}
(b) Show that the point (x,y)= (3,1) lies on the curve defined by the equation in part (a), and find the slope of the tangent line
Algebra.Com
Question 592647: (a) Find dy/dx for
(b) Show that the point (x,y)= (3,1) lies on the curve defined by the equation in part (a), and find the slope of the tangent line at this point.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Take derivative of both sides with respect to x (note that since y is a function of x, you have to use the chain rule).
(4y^3)\frac{dy}{dx} + \frac{1}{2}(2x+3y)^{-\frac{1}{2}} (2 + 3 \frac{dy}{dx}) = 0)
Solve algebraically for dy/dx.
For part b, it is easy to show that (3,1) is on the curve because if you replace x=3, y=1 into the equation you should get a true statement. To find dy/dx at (3,1), replace x=3, y=1 into your expression for dy/dx (which you will have found in part a).
RELATED QUESTIONS
Please help me solve this equation:
1. Determine dy/dx for y = x√x(5x^2 − (answered by Fombitz)
I have a question regarding finding the second derivative of a hyperbola...
Find the... (answered by Alan3354)
Hi Can somebody please help me with this problem
Confirm that the point P(1,1) lies on... (answered by Fombitz)
Find dy/dx of (3y^2/(1-3xy)) and find the point on the curve where dy/dx =... (answered by Edwin McCravy)
Q) Find dy/dx for each of the following.
a) y=-1/6(e^(-3x))+x(2x-1)
b)... (answered by Boreal)
Part of the graph to a curve has equation y=x³-15/2x²+12x-18.
(a) Find the coordinates (answered by solver91311)
A curve is such that dy/dx = 2(3x + 4)^3/2 - 6x - 8
a) Find d^2y/dx^2
b) Verify that... (answered by ikleyn)
Given that y = √4x-7 - 2/3(x-4), find dy/dx and show that d^y/dx^2 = -4/(4x-7)√4x-7... (answered by greenestamps)
Find dy/dX of the following.
a) y=-1/6(e^(-3x))+x^(2x-1)
b)... (answered by Alan3354)