Question

find dy/dx. yo do not need to simplify.

1. 4cos(x)sin(y)+tan(x/y)=1+x+y

2. x/y=cosx

Please show work.

Answer #1

1.Given that y = x + tan−1 y , find dy dx
2.Determine the equation of the tangent line to the curve y = (2
+ x) e −x at the point (0, 2)

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 dy/dx, given sin(x^2+y^2)=4xy
PLEASE , no Hospital Rule
and please check for comments later on in case there is
something no clear .
thanks

Find dy/dx if y= tan(sinx)

Solve the following
a)y=tan^-1 (sqrt((x+1)/(x+2)
b)y=ln(sin^-1(x))
c)d/dx[sec^-1(x)]=1/(x(sqrt(x^2 -1)
d)Find Y' tan^-1(x^2 y)=x+xy^2

Consider x^2 +sin(y)=4xy^2 +1
a.)Use Implicit differentiation to find dy/dx
b.) find an equation tangent of the line to the curve x^2
+sin(y)=4xy^2 +1 at (1,0)

Find an integrating factor and solve the O.D.E. 1 + (x/y −
sin(y) *dy/dx = 0.

using only words can you explain how to solve:
find dy/dx by implicit differentiation.
tan^-1 (x^2,y)=x+xy^2

please only answer if you can do all parts, show work and circle
answer
part 1)
Use implicit differentiation to find the first derivative of y
with respect to x.
ln(4y)=5xy
dy/dx=
part 2)
Find dy/dx by implicit differentiation.
3+8x=sin(xy^2)
Answer: dy/dx=
part 3)
Find dy/dx by implicit differentiation.
e^((x^2)y)=x+y
dy/dx=
part 4)
Find dy/dx by implicit differentiation.
sqrt(x+y)= 9+x^2y^2
dy/dx=
part 5)
Find dy/dx by implicit differentiation.
e^y=8x^2+7y^2
dy/dx=

Find the general solution and initial value solution: (cos x)dy
= -2y2(tan x)dx, y(0)=1/6

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