Question
What is wrong with the following reasoning???
f(x) = 2^x
f'(x) = x[2^(x-1)]
Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant.
The derivative of b^x, where b is a constant, is ln(b) * b^x
For a proof, see http://math2.org/math/derivatives/more/b^x.htm
f(x) = 2^x
f'(x) = x[2^(x-1)]
Although n x^(n-1) is the derivative of x^n, you cannot apply similar rules when x is the exponent and the number being raised to a power is a constant.
The derivative of b^x, where b is a constant, is ln(b) * b^x
For a proof, see http://math2.org/math/derivatives/more/b^x.htm