Question

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

Answer #1

differentiate.
a. e^xtan(x)
b. sin(1/sqrtx)
c. ln(e^x/sqrt(x^2)+3)
d. subscriptx tan(x)
e. f(secx) where f'(x)= x/ln(x)

Differentiate the function
y=ln(e-x +xe-x)
Find y and y"
y=ln(sec(3x)+tan(3x))
Use logarithmic differentiation to find the derivative
of the function.
y=(cos(9x))x
Use logarithmic differentiation to find the derivative
of the function.
y=(sin(9x))(lnx)

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, ...}

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

1. Find the general solutions
a. xy’ + ln(x)y = 0
b. xy’ - 3x = 0
2. Solve the initial value
a. xy’ + (1 + xcox(x))y = 0; y(pi/2) =
2

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

1) show that
tanh-1(x) = 1/2 ln (1+x/1-x)
2) show that
a) d/dx (cosh-1(x)) = 1/sqrt x2-1
b) d/dx (tanh-1(x)) = 1/1-x2
3) verify that y = A cosh(3x) + B sinh(3x) is a solution to the
equation y''-9y = 0

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.

solve differential equation ((x)2 - xy +(y)2)dx - xydy
= 0
solve differential equation (x^2-xy+y^2)dx - xydy =
0

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