What is Inx? If you are going by what is on a button on a calculator, that is ln x (LN), for natural logarithm.anthonyk2013 said:y=3x2Inx
If v = ln(x), then dv/dx = 1/x, not I/x.anthonyk2013 said:u=3x2
v=Inx
du/dx=6x
dv/dx=I/x
anthonyk2013 said:y=u*v
dy/dx=(u)(dv/dx)+(v)(du/dx)
dy/dx=(3x2)(I/x)+(Inx)(6x)
Can I simplify this further
Mark44 said:What is Inx? If you are going by what is on a button on a calculator, that is ln x (LN), for natural logarithm.
If v = ln(x), then dv/dx = 1/x, not I/x.
Please post homework-type problems in the Homework & Coursework section, not in the technical math sections. I am moving this thread.
The product rule is a mathematical rule used to calculate the derivative of a product of two functions. It states that the derivative of a product of two functions is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function.
The product rule is important because it allows us to find the derivative of complicated functions that are expressed as a product of two or more simpler functions. It is a fundamental rule in calculus and is used extensively in areas such as physics, engineering, and economics.
To use the product rule, you need to identify the two functions that are being multiplied together. Then, you take the derivative of each function separately and apply the formula: (first function)(derivative of second function) + (second function)(derivative of first function). This will give you the derivative of the original product function.
Yes, the product rule can be extended to more than two functions. For example, if you have a product of three functions, the formula becomes: (first function)(derivative of second function)(derivative of third function) + (second function)(derivative of first function)(derivative of third function) + (third function)(derivative of first function)(derivative of second function). This pattern can be extended to any number of functions.
The product rule and the chain rule are two different rules used to find the derivative of a function. The product rule is used when the function is expressed as a product of two or more functions, while the chain rule is used when the function is composed of two or more functions. In other words, the product rule deals with multiplication, while the chain rule deals with composition.