if y=log(1+tanx/1-tanx )^0.5 then prove dy/dx=sec^2x

if y=log(1+tanx/1-tanx )^0.5 then prove dy/dx=sec^2x

if y=log(1+tanx/1-tanx) then prove that dy/dx =sec^2x

Calculus Question - Please help An object is thrown from a height H above an uneven ground described by a height function h(x). Suppose that the object can be thrown with maximum velocity v at...

The answer which I got was (e^(-x))sin(x/2)-cos(x/2)(e^(-x)) However all the math solvers on the internet are giving different answers. Could you clear things up and tell...

I', really stuck on this one HW question: I have to show how dC/dt = (D * (d^2C/dx^2)) + P at steady state (so when cD/dt =0) equals: (d^2C/dz^2) + (Pa^2/D...

(Hint for h to be maximum, dh/dt=0)

then ∫ x f(x) dx =

The length of a rectangle is given by the function l(t)=6t+5 and its height is given by the function h(t)=the sq root of t, where t is time in seconds and the dimensions are in centimeters. Find...

find where (what are the coordinates) the tangent line to the graph of f(x)=(x+1)/(x-1) is parallel to the line whose equation is 2y+x=6

A fitness club sells its memberships at a fee of $100/month. The club sells 30 memberships per month. CEO of this club estimates that every $10 discount in membership fee, number of users will increase...

A cable company is to connect cable to a house. house is located 3 km from highway, and cable source is located 20km down the highway from the closest point to the house. The cost to lay the cable...

Suppose that the demand of a certain item is x=100e^(−0.02p) Evaluate the elasticity at 40:

So I was trying to find a solution to some unusual integral. Let say int(e^(sinx) dx). And then it came to my mind that it might exist a well defined function of x, f(x), such that lim n-> infinity...

A plane flying horizontally at an altitude of 4 mi and a speed of 465 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing...

the problem is stated as above. I'm just not sure where to start.

Two corridors 3m and 4m wide meet at right angles. Find the length of the shortest thin straight road that can pass horizontally around the corner.

A farmer’s barn is 60 feet long on one side. He has 150 feet of fence and wishes to build two adjacent rectangular pens of equal area along that side of his barn. What should be the arrangement and...

Take the above function. If x=1, the velocity is 0 and position is -22. FInd v(t) at any time. Find x(t) at any time. I have no clue how to answer this. Absolutely no...

VOLUME : A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 cm...

A curve has equation y=(x2+1)4+2(x2+1)3. Show that dy/dx=4x(x2+1)2 (2x2+5) and hence show that the curve has one stationary (critical) point. State the coordinates of the stationary...

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