OpenStudy (anonymous):

Differentiate the function: f(x)=5tan(x)cos(x)

OpenStudy (anonymous):

Tan x = Sin x/Cos x

OpenStudy (anonymous):

ok Im not sure what to do next

OpenStudy (anonymous):

Im here

OpenStudy (anonymous):

5 sinx/cosx-sinx?

OpenStudy (anonymous):

U want to diff f(x)=5tan(x)cos(x) and Tan x = Sin x/Cos x so sub it in, then its simple....

OpenStudy (anonymous):

I can't remember what to do afterwords.

OpenStudy (anonymous):

Maybe if u think a bit, it will come back to you....

OpenStudy (anonymous):

are tan(x) and cos(x) multiplied together in the beginning?

OpenStudy (anonymous):

OpenStudy (anonymous):

5(1/cos^2)-sin(x)?

OpenStudy (tkhunny):

Yes, that is simple. Too bad it will not lead to a correct result. As it is written, with that tangent, there are quite a few holes in the Domain. Everywhere cos(x) = 0, this function does not exist. If we promise to stay away from x = pi/2 + kpi, for k an integer, then we can proceed, but we will not get a derivative for these same values that are NOT in the Domain fo the function. NOW you can worrk about g(x) = 4*sin(x) which is not quite the same as f(x) = 5*tan(x)*cos(x)

OpenStudy (anonymous):

did you see what I wrote is that right?

OpenStudy (tkhunny):

Not sure what possessed me to write g(x) = 4*sin(x), since obviously it should have been g(x) = 5*sin(x). I'm not sure what you did, there. Working with g(x) and remembering the Domain, is MUCH simpler.