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What is the derivative of log Y?

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What is the derivative of log Y?

logy is a function of y, and y is a function of x. Then by chain rule ddx(logy)=ddy(logy)×ddx(y)=1y×dydx.

What is the implicit derivative of y?

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of our assumption that y may be expressed as a function of x.

How do you find the derivative of a log function?

To find the derivative of other logarithmic functions, you must use the change of base formula: loga(x)= ln(x)/ln(a). With this, you can derive logarithmic functions with any base. For example, if f(x)=log3(x), then f(x)=ln(x)/ln(3).

How do you find y using log differentiation?

Logarithmic Differentiation Steps

  1. Take the natural log of both sides.
  2. Use log properties to simplify the equations.
  3. Differentiate both sides using implicit differentiation and other derivative rules.
  4. Solve for dy/dx.
  5. Replace y with f(x).

How do you find the derivative of y?

Given y = f(x) g(x); dy/dx = f’g + g’f. Read this as follows: the derivative of y with respect to x is the derivative of the f term multiplied by the g term, plus the derivative of the g term multiplied by the f term.

What are some examples of derivatives?

Common examples of derivatives include futures contracts, options contracts, and credit default swaps. Beyond these, there is a vast quantity of derivative contracts tailored to meet the needs of a diverse range of counterparties.

How do you solve logarithmic differentiation?

How to Use Logarithmic Differentiation

  1. Take the natural log of both sides.
  2. Now use the property for the log of a product.
  3. Differentiate both sides. For each of the four terms on the right side of the equation, you use the chain rule.
  4. Multiply both sides by f (x), and you’re done.

How is the derivative of the natural log related?

The natural log is the inverse function of the exponential function. They are related by the following identities: The derivative of the natural logarithmic function (ln [x]) is simply 1 divided by x. This derivative can be found using both the definition of the derivative and a calculator.

Is the derivative of log 2 6 a constant?

The first term, log 2 6, is a constant, so its derivative is 0. The term on the top, log 2 e, is a constant. If we need a decimal value, we can work it out using change of base as follows:

How to convert ln x to natural logarithm?

Direct link to Enn’s post “Firstly log (ln x) has to be converted to the natur…” Firstly log (ln x) has to be converted to the natural logarithm by the change of base formula as all formulas in calculus only work with logs with the base e and not 10.

How to calculate the derivative of ln ( x )?

Firstly log (ln x) has to be converted to the natural logarithm by the change of base formula as all formulas in calculus only work with logs with the base e and not 10. Hence log (ln x) = ln (ln x) / ln (10) and then differentiating this gives [1/ln (10)] * [d (ln (ln x)) / dx].