d/dx cos (2x - 3) = 2 sin (3 - 2x) I get why it is 2 sin (... but I do not understand why it is not negative 2 sin (... and why the signs of 2x and 3 were switched. Please walk me through it! As a side note: My book doesn't really explain differentiation of sin (ax), it just kind of assumes I will know what to do with u-substitution...

Question

d/dx cos (2x - 3) = 2 sin (3 - 2x)  I get why it is 2 sin (... but I do not understand why it is not negative 2 sin (... and why the signs of 2x and 3 were switched. Please walk me through it! As a side  note: My book doesn't really explain differentiation of sin (ax), it just kind of assumes I will know what to do with u-substitution...

ganeshie8 · Answer

the short answer is :

`sin(-something) = -sin(something)`

ganeshie8 · Answer

`sin` is an odd function so, f(-x) = -f(x)

ganeshie8 · Answer

so, 

sin(2x-3)  =  sin(-(3-2x)) = -sin(3-2x)

anonymous · Answer

Oh so that's the simplified answer! They just did the above example in reverse... Thanks!

ganeshie8 · Answer

however below answer looks good to me as it is more direct :

d/dx cos (2x - 3)  =  -2sin(2x-3)