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stat643
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i can differentiate most other simple functions.. .though can someone please help me to understand why the derivative of f(x)=-5/3x is simply 5/3x^2?
Then you should be able to solve this as that's all that's needed.stat643 said:1/x = x^-1 and yes i can differentiate functions in the form x^n
The derivative of a function is a measure of its rate of change at a specific point. In this case, the function -5/3x represents a straight line with a slope of -5/3. When finding the derivative, we use the power rule which states that for a function of the form y = ax^n, the derivative is given by dy/dx = anx^(n-1). Applying this rule to -5/3x, we get a derivative of -5/3x^(1-1) = -5/3x^0 = -5/3. This is the constant slope of the original function. However, since the derivative is a function of x, we can rewrite it as -5/3x^1 = -5/3x, which is equivalent to 5/3x^2.
No, the derivative of -5/3x is already in its simplest form. It is important to note that the derivative is only a measure of the slope of the function at a specific point and may not represent the entire behavior of the function.
To find the derivative of -5/3x, we use the power rule which states that for a function of the form y = ax^n, the derivative is given by dy/dx = anx^(n-1). In this case, we have a constant value of -5/3, so the derivative is simply -5/3x^(1-1) = -5/3x^0 = -5/3.
No, the derivatives of -5/3x and 5/3x are not the same. The negative sign in front of -5/3x represents a negative slope, while the positive sign in front of 5/3x represents a positive slope. This is reflected in their respective derivatives, which are -5/3 and 5/3, respectively.
Yes, the derivative of -5/3x can be negative. As mentioned before, the negative sign in front of -5/3x represents a negative slope. This means that as x increases, the value of -5/3x decreases, resulting in a negative derivative. However, the derivative can also be positive or zero, depending on the value of x and the function's behavior.