The derivative of cot(x) is -csc2(x).
(Which is the same as -1/sin2(x).)
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The derivative of csc(x) is -cot(x)csc(x).
d/dt cot (t) dt = - cosec2(t)
First note that this not the graph of y = |cot(x)|.The equivalent equations for |y| = cot(x) or cot(x) = |y| arecot(x) = -y or cot(x) = +ySo plot y = cot x and then reflect all the points in the x-axis.
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
The derivative of 3cos(x) is -3sin(x). This can be found using the chain rule, which states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, the derivative of cos(x) is -sin(x), and when multiplied by the constant 3, we get -3sin(x) as the derivative of 3cos(x).