Write ##\ \sqrt{x} \ ## as ##\displaystyle \ x^{1/2} \ ## .By the way, the word in English is differentiate, not derive.Arnoldjavs3 said:Homework Statement
derive this function
f(x) = (2x + x^3) / sqrt(x)Homework Equations
The Attempt at a Solution
how can i derive this without using quotient rule? my prof is asking to do so without using it.
I
It's not correct, but you're not too far off. And you should end up with two terms, so I don't understand what you're asking about accounting for the binomial.Arnoldjavs3 said:Okay using that I got something like x^5/2 + x^1/2. It doesn't seem correct, how would i account for the binomial on the numerator?
What do you get if you carry out the division below?Arnoldjavs3 said:would I write another expression for x such as x^h?
Arnoldjavs3 said:edit: I just misunderstood the question... I am allowed to use both the quotient and product rule.
No, that's not even close. There's some very basic algebra that you need to review. If you don't, you absolutely won't be able to do calculus.Arnoldjavs3 said:alright... I got it.
I simply just subtract the exponents from the numerator and denominator so it became (2 + 5x^2) / 2x^1/2
A derivative is a mathematical concept that measures the rate of change of one quantity with respect to another. It is often referred to as the slope of a curve at a given point.
The derivative of a function is found by taking the limit of the average rate of change as the interval between two points approaches zero. This can be done using the power rule, product rule, quotient rule, or chain rule, depending on the complexity of the function.
Finding a derivative is useful in many areas of science, such as physics, engineering, and economics. It allows us to understand how a system changes over time and to make predictions about its future behavior.
One example of a real-world application of derivatives is in calculating the velocity of an object at a particular point in time. By finding the derivative of the object's position function, we can determine its instantaneous velocity at that moment.
While derivatives are a powerful tool in mathematics and science, there are some limitations to their use. For example, they may not be able to accurately describe systems with abrupt changes or discontinuities. Additionally, they may not be appropriate for nonlinear or chaotic systems.