Simple differentiation question

In summary, the question is asking for the derivative of (4^x)/(ln4). After several attempts, the answer is determined to be 4^x. The working process involves using the quotient rule, taking the derivative of a constant, and factoring the constant out.
  • #1
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"Simple" differentiation question

There is a question which is as follows:

(4^x)/(ln4)

I have tried many times to get the answer but with no success, would someone be so kind as to show me how to do it?

The answer is:

4^x

My working is as follows:

f(x) = (4^x)/(ln4)
F'(x) = ((ln 4 * ln 4 * 4^x) - (4^x - (1/4))) / ((ln 4)^2)
f'(x) = (4^x) - ((4^x * (1/4)) / ((ln 4)^2))

...help?
 
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  • #2
F'(x) = ((ln 4 * ln 4 * 4^x) - (4^x - (1/4))) / ((ln 4)^2)
f'(x) = (4^x) - ((4^x * (1/4)) / ((ln 4)^2))
You cannot use quotient rule here.

Let y = 4x

take ln on both sides

ln y = x ln 4

Take the first derivatives on both sides

y'/y = ln 4

y' = y ln 4 = 4x ln 4

So,

F(x) = (4^x)/(ln4)

F'(x) = (1/ln 4) * y' (since the denominator is a constant) = 4^x
 
  • #3
Well, you can use the quotient rule here if you remember that the derivative of a constant (like ln 4) is zero.

(of course, you should just factor the constant out like you suggested)
 
  • #4
Ahh yip, got it. Thanks guys :D
 

What is differentiation?

Differentiation is a mathematical process used to find the rate of change of a function with respect to its independent variable. It involves finding the derivative of a function.

What is the purpose of differentiation?

The purpose of differentiation is to determine the slope or rate of change of a function at a particular point. It is used in many fields such as physics, economics, and engineering to analyze and solve real-world problems.

What is the difference between differentiation and integration?

Differentiation is the process of finding the derivative of a function, which gives the rate of change of the function. Integration, on the other hand, is the reverse process of differentiation and is used to find the original function from its derivative.

What are the basic rules of differentiation?

The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. These rules are used to find the derivative of different types of functions.

What are the applications of differentiation?

Differentiation has many practical applications, including optimization problems, curve sketching, and finding maximum and minimum values of a function. It is also used in physics to analyze motion and in economics to determine marginal cost and revenue.

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