I would appreciate if someone could check my solutions for the following:
find dy/dx of y=sqrt(sec(5x))
my answer is (5/2)(sec5xtan5x)^(-1/2)
find dy/dx of y+sin(y)=x
my answer is (1/(1+cos(y)))
Thank you for looking , thank you even more if you help!
The image didn't load the first time I viewed your response, I thereby withdraw my previous comment, and submit a new one in it's place:
Thanks a lot
I have another question, what software do you use to type in all the math formulas? It seems to work pretty well
I'm having trouble getting the following word question:
A police officer in a patrol car is approaching an intersection at 25m/s. When he is 210 m from the intersection, a truck crosses the intersection travelling at right angles to the police car's path at a rate of 25m/s. If the oficer focusses his spotlight on the truck, how fast is the light beam turning 3 seconds later assuming that both vehicles continue at their same rates.
I would appreciate if someone could take a quick look at this question, maybe just give me a hint of what kind of approach to take, I have a feeling I can figure it out once I have a start.
The following two I thought I had figured out, but then I checked my answer with a graphing calculator and it didn't make any sense.
Find dy/dx of 1-2cos^2(x) = 4sin(x)cos(x)+y^2
I simplified this one to sin^2(x) = sin(4x)+y^2
and then tried to differentiate from there but it didn't work out, and I tried to differentiate the original as well. Was the original simplification incorrect?
Find dy/dx of (1/(1+cos(x)))
I tried this out and had something that looked good, but then I checked with a calculator and the derivative didn't mirror the slope of the equation at all.
Thanks for looking. Hopefully I can get all this stuff figured out soon and answer some questions for other people.
you asked for a hint, so that's what i'll give. see the diagram below, this is a related rates problem.
yes, the simplification was incorrect.Find dy/dx of 1-2cos^2(x) = 4sin(x)cos(x)+y^2
I simplified this one to sin^2(x) = sin(4x)+y^2
and then tried to differentiate from there but it didn't work out, and I tried to differentiate the original as well. Was the original simplification incorrect?
1 - 2cos^2(x) = 4sin(x)cos(x) + y^2 ..........since cos(2x) = 2cos^2(x) - 1 = -(1 - 2cos^2(x)) and sin(2x) = 2sin(x)cos(x)
=> -cos(2x) = 2sin(2x) + y^2
=> y^2 = -cos(2x) - 2sin(2x)
try differentiating now
y = 1/(1 + cos(x)) = (1 + cos(x))^-1Find dy/dx of (1/(1+cos(x)))
By the chain rule
=> dy/dx = -(1 + cos(x))^-2 * (-sin(x))
=> dy/dx = sin(x)(1 + cos(x))^-2
I'm working on that word problem currently. I would appreciate if someone could take a quick look at my solutions to the following problems. I have a feeling I messed something up, because I'm good at messing things up.
dy/dx of y=[csc^2(x)]-[3x^2][cot^2(x)]
dy/dx=2(cscx)d/dx(cscx) - 6x(2(cotx))d/dx(cotx)
dy/dx=2(cscx)(-cscxcotx) - 12x(cotx)(-csc^2(x))
dy/dx of y = csc((x^2-2)^3)
dy/dx= [-csc(x^2-2)^3][cot(x^2-2)^3][d/dx(x^2-2)^3]
dy/dx= [-csc(x^2-2)^3][cot(x^2-2)^3][3(x^2-2)^2][d/dx(x^2)]
dy/dx= [-csc(x^2-2)^3][cot(x^2-2)^3][3(x^2-2)^2][2x]