Find dy/dx if y^2 + 4 = x^2 + sin(11xy) Perform the initial implicit differentia

Question

Find dy/dx if y^2 + 4 = x^2 + sin(11xy) Perform the initial implicit differentiation, using the "d" notation for your derivative, along with x, y, and any trig-functions, as needed, as you are performing the left hand and right hand derivative steps: solve the above equation for dy/dx: Find dy/dx at the point (2, 0): (Give the normal line to the graph at the point (2, 0) in the form y - mx + b. Find the derivative of the function, and write the final answer in terms of only sine. f(x) = cot(x)/sin(x)

Explanation / Answer

16. given y2 + 4 = x2 + sin(11xy)

differntiate with respect to x

2ydy/dx = 2x + cos(11xy)*d/dx(11xy)

2y dy/dx = 2x + cos(11xy) ( 11y + 11x dy/dx)

dy/dx( 2y - 11x cos(11xy) ) = 2x + 11ycos(11xy)

dy/dx = [ 2x + 11ycos(11xy) ]/[ 2y - 11x cos(11xy) ]

b.

at(2,0), dy/dx = [ 4 + 0]/[-22] = -2/11

normal slope = -1/(-2/11) = 11/2

equation of normal at (2,0) is

y-0=11/2(x-2)

y = 11x/2 - 11

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