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Is logarithmic differentiation specially useful when dealing with functions with exponent that also depend on x?
Wiki User
∙ 11y ago
Yes. For example, to differentiate y = (x^2 + 1)^x, we take the natural log of both sides.ln(y) = ln((x^2 + 1)^x)
Bring down the exponent.
ln(y) = x ln(x^2 + 1)
Differentiate both sides.
dy/y = ((2x^2)/(x^2 + 1) + ln(x^2 + 1)) dx
Substitute in y = (x^2 + 1)^x.
dy/((x^2 + 1)^x) =((2x^2)/(x^2 + 1) + ln(x^2 + 1)) dx
Solve for dy/dx.
dy/dx = ((x^2 + 1)^x)((2x^2)/(x^2 + 1) + ln(x^2 + 1))
Wiki User
∙ 11y ago
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What is the second derivative of x raised to the 1 divided by x?
To calculate the derivate of a power, where both the base and the exponent are functions of x, requires a technique called logarithmic derivation. I'll leave the details to you; it is not particularly difficult. You can look up "logarithmic differentiation" in the Wikipedia for some examples.
Why are logarithmic functions used?
A log is just another way to write an exponent. Log functions are used to make some very complicated computations easier.
What is the inverse of an exponent function?
It is the logarithmic function.
What is LOG BAN?
LOG BAN is an acronym used to describe logarithmic functions. A log is an exponent to which another fixed value must be raised in order to produce that number.
The advantages of exponential and logarithmic functions?
logarithmic function is used to simplify complex mathematical calculation. FOR example- Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact-important in its own right-that the logarithm of a product is the sum of the logarithms of the factors:if someone needs to calculate value of 2.33153.017 he can calculate it by using logarithmic function.The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3
What is the second derivative of x raised to the 1 divided by x?
To calculate the derivate of a power, where both the base and the exponent are functions of x, requires a technique called logarithmic derivation. I'll leave the details to you; it is not particularly difficult. You can look up "logarithmic differentiation" in the Wikipedia for some examples.
Why are logarithmic functions used?
A log is just another way to write an exponent. Log functions are used to make some very complicated computations easier.
What is the inverse of an exponent function?
It is the logarithmic function.
What is LOG BAN?
LOG BAN is an acronym used to describe logarithmic functions. A log is an exponent to which another fixed value must be raised in order to produce that number.
The advantages of exponential and logarithmic functions?
logarithmic function is used to simplify complex mathematical calculation. FOR example- Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact-important in its own right-that the logarithm of a product is the sum of the logarithms of the factors:if someone needs to calculate value of 2.33153.017 he can calculate it by using logarithmic function.The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3
What exponential equation is equivalent to the logarithmic equation e exponent a equals 47.38?
The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)The given equation is exponential, not logarithmic!The logarithmic equation equivalent to ea= 47.38 isa = ln(47.38)ora = log(47.38)/log(e)
What is meaning of exponent with variable?
That you have an exponential function. These functions are typical for certain practical problems, such as population growth, or radioactive decay (with a negative exponent in this case).
How do we change from logarithmic form to exponential form?
Logb (x)=y is called the logarithmic form where logb means log with base b So to put this in exponential form we let b be the base and y the exponent by=x Here is an example log2 8=3 since 23 =8. In this case the term on the left is the logarithmic form while the one of the right is the exponential form.
Why do exponential functions not equal zero?
exponent of any number is more than 0
Write function integerpower that return the value of base exponent?
write a scripting to return values in functions
How do we change from logarithmic form to exponential form if it doesn't have a exponent?
ln x = 3 becomes x = e3 for natural logarithms e is the base the side opposite the log side becomes the exponent. ln 3 = x ... use a calculator or log table to find the value of x same for logs of any other base.
What is the smallest raised number in a power that tells how many times the base is used as a factor?
The exponent.
