Derivative of a logarithmic function

In summary, the derivative of a logarithmic function is the slope of the tangent line at any given point on the function's graph and represents the rate of change of the function at that point. To find the derivative, the power rule can be used and the domain and range are all positive and real numbers, respectively. The chain rule can also be used to find the derivative and it has various real-world applications, such as determining growth rates in finance, radioactive decay rates in physics, and population growth models in biology.
  • #1
magnifik
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Homework Statement


Compute the derivative:
d/dx log base 10 (x^3 + x^2)


Homework Equations





The Attempt at a Solution


(3x^2 + 2x)/(ln 10)(x^3 + x^2)
seems a little off.. not sure though

thanks for the help in advance! (:
 
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  • #2
That looks correct to me.
 

Related to Derivative of a logarithmic function

1. What is the derivative of a logarithmic function?

The derivative of a logarithmic function is the slope of the tangent line at any given point on the function's graph. It represents the rate of change of the function at that point.

2. How do you find the derivative of a logarithmic function?

To find the derivative of a logarithmic function, you can use the power rule, which states that the derivative of logb(x) is 1/(xlnb).

3. What is the domain and range of the derivative of a logarithmic function?

The domain of the derivative of a logarithmic function is the same as the original function, which is all positive real numbers. The range, however, is all real numbers.

4. Can you use the chain rule to find the derivative of a logarithmic function?

Yes, you can use the chain rule to find the derivative of a logarithmic function. For example, if the logarithmic function is logb(u), the derivative would be 1/(ulnb) * du/dx.

5. How is the derivative of a logarithmic function used in real-world applications?

The derivative of a logarithmic function is used in many real-world applications, including finance, physics, and biology. In finance, it can be used to determine the growth rate of investments. In physics, it can be used to calculate the rate of radioactive decay. In biology, it can be used to model population growth.

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