How do you differentiate 2^x?
We can differentiate this implicitly by writing the question as:y = 2x Then we take the log of both sides:ln(y) = ln(2x)Using the rules of logartithms this can be written as:ln(y) = x ln(2)Now we can differentiate this easily:y-1 dy/dx = ln(2)We can now re-arrange to get:dy/dx = y ln(2)And finally we can substitute y to get our answer:dy/dx = 2x ln(2)So we have shown that the derrivative of 2x is simply 2x multiplied by ln(2)
AC
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Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.