Do you really mean ##n * x^n - 1##? That's what you wrote. As inline text, use parentheses -- n*x^(n - 1)5P@N said:
Yes. ##d/dx(2x^2) = 4x##.5P@N said:
Maybe they're working a different problem.5P@N said:
I can think of many reasons, but none of them involve mathematics.5P@N said:
Contrary to much popular opinion, the opposite of integration is differentiation, not derivation. You can derive the quadratic formula using the completion of squares technique, but you differentiate ##2x^2## to get the derivative, 4x. Yes, English is weird...5P@N said:And just for the record: I meant DERIVATION, not integration.
Thanks for clarifying. I sometimes get confused because the result of differentiation is a derivative (obeying the product rule) and the result of integration is an anti-derivative. Is that correct or am I still confusing terms?Mark44 said:
No, you have it right.fresh_42 said:
A derivative is a mathematical concept that represents the instantaneous rate of change of a function at a specific point. It measures how much a function changes with respect to its input variable.
To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, and chain rule. Alternatively, you can also use the definition of a derivative, which involves taking the limit of the difference quotient as the change in the input variable approaches zero.
Yes, the derivative of a function is always unique. This means that no matter which method you use to find the derivative, you will always get the same result.
The derivative of 2x^2 is 4x. This can be found using the power rule, which states that the derivative of x^n is nx^(n-1). In this case, n=2, so the derivative is 2*2x^(2-1) = 4x.
There is confusion about the derivative of 2x^2 because it can also be written as 2x*x, which can be interpreted as either 2*(x*x) or (2x)*x. In the first case, the derivative is 2x, while in the second case, the derivative is 4x. This is due to the ambiguity of the multiplication symbol, which is why it is important to use proper parentheses when writing mathematical expressions.