Question

a. *If
*y=**x**3**+7/**x^**2/3*
, then find *dy/**dx* . Make sure your answer is
fully simplified.

b. *If *y=**5x-8**4x+3* , then
find *dy/**dx* .

c. *If
*x**=(**x**2**-5x+3)(2**x**2**+4)*
, then find *f ‘(x).*

Please neatly show your work.

Answer #1

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 if y= (x^3+5x)(4x^2+10)^9

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

Find the solution of the following differential
equation:
(?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

Evaluate C (y + 6 sin(x)) dx + (z2 + 2 cos(y)) dy + x3 dz where
C is the curve r(t) = sin(t), cos(t), sin(2t) , 0 ≤ t ≤ 2π. (Hint:
Observe that C lies on the surface z = 2xy.) C F · dr =

let Q1= y(2) and Q2= y(3) where y=y(x) solves...
(dy/dx) + (2/x)y
=5x^2
y(1)=2

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

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.

Exercise 178 Further problems on equations of the form dy
dx=f(x). In Problems 1 to 5, solve the differential
equations.
1.dy/ dx = cos4x−2x
2. 2xdy/dx =3−x3
3.dy/dx +x=3, given y=2 when x=1
4. 3d/ dθ +sin θ=0, given y=2/3when θ=π 3
5.1/ex +2=x−3dy/dxgiveny= y=1 when x=0.
6. The gradient of a curve is given by: dy dx + x2 2 =3x
engineering mathematics

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