The rule for the log of a reciprocal follows from the rule for the power of negative oneĪnd the above rule for the log of a power. Usual functions are allowed: sine, cosine, tangent, logarithm (log), exponential, root, etc. The derivative of the exponential function is equal to the value of the function. The logarithm with base $b$ is defined so thatįor any given number $c$ and any base $b$.įor example, since we can calculate that $10^3=1000$, we know that $\log_ to conclude that This tool calculates the derivative of a function. Detailed step by step solutions to your Logarithmic differentiation problems online. Just like we can change the base $b$ for the exponential function, we can also change the base $b$ for the logarithmic function. Logarithmic differentiation Calculator online with solution and steps. To get all answers for the above problems, we just need to give the logarithm the exponentiation result $c$ and it will give the right exponent $k$ of $2$. In other words, the logarithm gives the exponent as the output if you give it the exponentiation result as the input. Log base 2 is defined so thatįor any given number $c$. We define one type of logarithm (called “log base 2” and denoted $\log_2$) to be the solution to the problems I just asked. But, what if I changed my mind, and told you that the result of the exponentiation was $c=4$, so you need to solve $2^k=4$? Or, I could have said the result was $c=16$ (solve $2^k=16$) or $c=1$ (solve $2^k=1$).Ī logarithm is a function that does all this work for you. To calculate the exponent $k$, you need to solveįrom the above calculation, we already know that $k=3$. Instead, I told that the base was $b=2$ and the final result of the exponentiation was $c=8$. Let's say I didn't tell you what the exponent $k$ was. We can use the rules of exponentiation to calculate that the result is Explanation: The derivative of The derivative of a logarithmic function is the.
![derivative of log calculator derivative of log calculator](https://i.stack.imgur.com/T9AeU.png)
The result is some number, we'll call it $c$, defined by $2^3=c$. So This derivative calculator takes account of the parentheses () of a. If we take the base $b=2$ and raise it to the power of $k=3$, we have the expression $2^3$. You can also get a better visual and understanding of the function by using our graphing tool. Detailed step by step solutions to your Properties of Logarithms problems online with our math solver and calculator. The Derivative Calculator supports solving first, second., fourth derivatives, as well as implicit differentiation and finding the zeros/roots. Properties of Logarithms Calculator online with solution and steps. In other words, if we take a logarithm of a number, we undo an exponentiation. Enter the function you want to find the derivative of in the editor.