Calculus

posted by .

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. CALCULUS

    what is the derivative of ln(x-1)? If you are studying the calculus of logarithms your question surprises me, since that is one of the most basic ones in that topic. in general if y = ln("anything") then y' = 1/"anything" * derivative
  2. Calculus

    If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x). My reasoning is that 'undoing' the derivative gives me the derivative. Eg is 1/3x^3 an integral of x^2?
  3. Math differentiation

    Can somebody please check these over for me?
  4. Calculus

    f(x)=sin^(7)x The 7 is an exponent and the x is not. Find the derivative.
  5. Genes

    Genetics and what we inherit from our biological parents play a significant role in our intelligence level. In fact, researcher have found that: a) adotpted children are more similar in IQ to their adoptive parents than to their birth …
  6. College Calculus 1

    We have to find the first and second derivative of f(x)=x^(2/3)(6-x)^(1/3) I have the first derivative as being (4-x)/(x^(1/3)(6-x)^(2/3)) And that I know is right. The second derivative is -8/(x^(4/3)(6-x)^(5/3)) I did all the work …
  7. Math 9

    use exponent rules to simplify. Write as a single power, don't need to find the value. [ (11/20)^4 x (11/20)^-8]^5 and (11/20)^-6 you cant leave an number to the power of a negative exponent. You have to change it like this ex : 2^-3 …
  8. Calculus Derivative

    I'm trying to calculate the derivative of this: P= mv/ sqrt(1-v^2/c^2)where m and c are constants, and v depends on t. I know about the chain and product rules but I'm not even sure where to start. :/ Thank you for your help.
  9. Math-Calculus

    Hi, I am trying to figure out what the limit as h approaches 0 of (1-2h)^(1/h) is. I am unfamiliar with the process I am supposed to use to solve this limit. I have just been reasoning out this limit, but I keep getting the answer, …
  10. Calculus

    If I derive the following, d/dt((a)S(t^2) of (s)^(1/2)ds with S being integral notation (a) being at the bottom of the notation and being a constant (t^2) being at the top of the notation ..I first apply the fundamental theorem of …

More Similar Questions