the derivative of 1x would be 1 the derivative of x to the power of 1 would be 1. the derivative of x+1 would be 1 the derivative of x-1 would be 1
im not sure what you are asking, but however you put it, it's 1.
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The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
x^0 = 1 for all x. The derivative of 1 is always zero.
The derivative of cot(x) is -csc2(x).(Which is the same as -1/sin2(x).)
y = ln (x) dy/dx = 1/x
sqrt(x) = x^(1/2) The derivative is (1 / 2) * x^(-1 / 2) = 1 / (2 * x^(1 / 2)) = 1 / (2 * sqrt(x))