Any monomial in the format:
axn
has a derivative equal to:
nax(n - 1)
In this case, "a" is equal to 1 and "n" is equal to 2. So the derivative of x2 is equal to 2x.
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The antiderivative of x/(x2-1) is ln(x2-1)/2. Proof: (ln(x2-1)/2)' = (1/(x2-1))*(x2-1)'/2=1/(x2-1)*(2x/2)=x/(x2-1).
if x2 + 7 = 37, then x2 = 29 and x = ±√29
I'm assuming your question reads "What is the derivative of 3cos(x2)?" You must use the Chain Rule. The derivative of cos(x2) equals -sin(x2) times the derivative of the inside (x2), which is 2x. So... d/dx[3cos(x2)] = -6xsin(x2)
In ordinary mathematics, assuming that x = X and that X2 denotes x2 or x-squared, there cannot be a counterexample since the statement is TRUE. However, there are two assumptions made that could be false and so could give rise to counterexamples. 1. x is not the same as X. If, for example X = 4x then X = -20 so that X2 = 400. 2a. X2 is not X2 but X times 2. In that case X2 = -10. 2b. X2 is x2 modulo 7, for example. Then X2 = 4.
x2 = 6482 = 64x = 8