You use the same power formula which you use for other powers of x, so the derivate is (1/2)x-1/2. This is the same as 1 / (2 times square root of x).
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The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
The derivative of tan(x) is sec2(x).(Which is the same as 1/cos2(x).
1/x = x-1d/dx(x-1) = -x-2 = -1/x2