Question

find dy/dx

a. (x+y)^4 =4y-9x

b. y= (x +6)^2x

c. y= cos^-1 (3x^2 -5x +1 )

Answer #1

Use implicit differentiation to find dy/dx of:
(x+y)4=4y-9x

Solve the differential equation (5x^4 y^2+ 2xe^y - 2x cos (x^2)) dx
+ (2x^5y + x^2 e^y) dy = 0.

1) Differentiate the function
y= 1/ (9x-8)6
2) Find the derivative of dy/dx of the given function
y= x3(2x-9)7
3) Differentiate the function
y=(4x-4)2(2-x5)2
4) Differentiate the given function
y=(x+4/x-9)8
5) Find the indicated derivative
d/dt ((4t-8)5/t+6)

Find dy/dx by implicit differentiation:
A.). x^4 + y^3 = 3
B.). 5x^2 +3xy - y^2 =7
C.) x^3(x+y) = y^2(4x-y)

Find dy dx/dy implicit differentiation. (x + y^2)10 = 9x^2 +
2

Consider the following. y = 6x^4 − 5x − 1/4 − x^2
A)Find the value of y when x = 1.
y(1) =
B Find dy/dx .
dy/dx =
C Find the exact value of dy/dx when x = 1.
dy/dx =
D Write the equation of the tangent line to the graph of y = 6x4
− 5x − 1 4 − x2 at x = 1. Check the reasonableness of your answer
by graphing both the function and...

find dx/dx and dz/dy
z^3 y^4 - x^2 cos(2y-4z)=4z

y = (6 +cos(x))^x
Use Logarithmic Differentiation to find dy/dx
dy/dx =
Type sin(x) for sin(x)sin(x) ,
cos(x) for cos(x)cos(x), and so on.
Use x^2 to square x, x^3 to cube
x, and so on.
Use ( sin(x) )^2 to square sin(x).
Use ln( ) for the natural logarithm.

Find the derivative of y=x^3x using the methods of example 6
dy/dx=

Consider the linearly independent set of vectors
B= (-1+2x+3x^2+4x^3+5x^4, 1-2x+3x^2+4x^3+5x^4,
1+2x-3x^2+4x^3+5x^4, 1+2x+3x^2-4x^3+5x^4, 1+2x+3x^3+4x^3-5x^4)
in P4(R), does B form a basis for P4(R) and why?

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