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If a simple constant, what is the derivative of y=x⁽³⁾

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User Vijayk
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The derivative of the function y = x³ can be found using the power rule for differentiation.The power rule states that if you have a function of the form y = x^n, where n is a constant, then the derivative of y with respect to x is given by:dy/dx = n * x^(n-1)In this case, the constant is 3, so the derivative of y = x³ would be:dy/dx = 3 * x^(3-1)Simplifying further:dy/dx = 3 * x²So, the derivative of y = x³ is dy/dx = 3x².To understand this concept better, let's consider an example. Suppose we have the function y = x³.If we take the derivative of this function, dy/dx, we are essentially finding the rate at which the function is changing with respect to x at any given point. In other words, we are finding the slope of the tangent line to the curve of the function at that point.Let's say we want to find the derivative of y = x³ at x = 2.Using the derived formula, dy/dx = 3x², we can substitute x = 2:dy/dx = 3 * (2)²= 3 * 4= 12So, at x = 2, the derivative of y = x³ is 12. This means that at that specific point, the function is changing at a rate of 12 units for every unit change in x.I hope this explanation helps you understand the derivative of y = x³.

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User BionicOnion
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