d/dt cot (t) dt = - cosec2(t)
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Assume that the expression is: y = 9e^(t) Remember that the derivative of e^(t) with respect to t is e^(t). If we take the derivative of the function y, we have.. dy/dt = 9 d[e^(t)]/dt = 9e^(t) Note that I factor out the constant 9. If we keep the 9 in the brackets, then the solution doesn't make a difference.
If it is with respect to t: 1 If it is with respect to some other variable (x for example): (dt)/(dx), which is literally read "the derivative of t with respect to x"
The derivative of cot(x) is -csc2(x).(Which is the same as -1/sin2(x).)
The derivative of csc(x) is -cot(x)csc(x).
Which expression is equivalent to cot t sec t