Please help & please show step-by-step, thx, appreciate it.
Below are notes my instructor gave for this assignment that are relative and important. The problems are below. There is 1 problem at the bottom of the page. Thank you.
When differentiating keep in mind the variable with respect you differentiate. For example, the
THE DIFFERENTIATION OF ALGEBRAIC FUNCTIONS
Use implicit differentiation to find the dy/dx:
3xy + x2y2 = 1
xy1/2 - 2x + y = 8
(x + y)3 = x3 + y3
3y2 + 5x2 -2x = 5
y4 = x3y2 + x2y3 - 3
Find the indicated higher order derivative of the following functions:
1. Find the 2nd derivative of f(x) = 7x^5 - 4
Consider this equation: x2 - 2xy + 4y2 = 64
A) write an expression for the slope of the curve at any point (x,y)
B) Find the equation of the tangent lines to the curve at the point x = 2
C) find d2y/dx2 at (0,4)
A circle of radius 3 inches is inside a square with 12-inch sides (see figure below). How fast is the area between the circle and square changing if the radius is increasing at 4 inches per minute and the sides are increasing at 2 inches per minute?
Find dy/dx in two way (a) by differentiating implicitly and (b) by
See attached file for full problem description.
1. Determine dy/dx for each of the following relations.
2. Determine the slope of the curve 2x3+2y3-9xy=0 at the point (1,2).
3. Find dy for the relation 4x2+y2=16 using each of the following methods.
i) Solve for y explicitly as a f