# Thread: Thinking and Inquiry Problem, Logarithmic Differentiation

1. ## Thinking and Inquiry Problem, Logarithmic Differentiation

Hey guys, this is my first post and of course first question to ask of calculus

Alright well I had this test and we had this very difficult question that I could not solve, it was in the hardest section.

The question is as follows:
A projectile thrown over level ground, at an angle x to the ground, has a range R given by R = (v^2 / g)(sin2x), where v is the initial speed, in meters per second, and g = 9.8m/s^2. Determine the angle of proection x for which the range is maximum.

So I began to isolate for v^2 and then use log differentiation.

R(g) = v^2(sin2x)
v^2 = Rg / sin2x

R = (v^2 / g)(sin2x)
R = ((v^2)(sin2x) / g)
ln R = ln v^2 + ln Sin2x - ln g
dR / dx = [(1 / v^2) + (1 / sin2x) - (1 / g)] (v^2(sinx) / g)

So im pretty sure that derrivative is right but as of this i am clueless on what to do. Any help is really appreciated, even a guideline so I could figure out the rest myself. Thanks.

2. Originally Posted by vexon
Hey guys, this is my first post and of course first question to ask of calculus

Alright well I had this test and we had this very difficult question that I could not solve, it was in the hardest section.

The question is as follows:
A projectile thrown over level ground, at an angle x to the ground, has a range R given by R = (v^2 / g)(sin2x), where v is the initial speed, in meters per second, and g = 9.8m/s^2. Determine the angle of proection x for which the range is maximum.

So I began to isolate for v^2 and then use log differentiation.

R(g) = v^2(sin2x)
v^2 = Rg / sin2x

R = (v^2 / g)(sin2x)
R = ((v^2)(sin2x) / g)
ln R = ln v^2 + ln Sin2x - ln g
dR / dx = [(1 / v^2) + (1 / sin2x) - (1 / g)] (v^2(sinx) / g)

So im pretty sure that derrivative is right but as of this i am clueless on what to do. Any help is really appreciated, even a guideline so I could figure out the rest myself. Thanks.
this does not require logarithmic differentiation, in fact, it doesn't even require calculus.