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candynrg
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How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)
candynrg said:How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)
PhysicsinCalifornia said:For the power rule, for
[tex]f(x)g(x) [/tex], the derivative is [tex]f'(x)g(x) + g'(x)f(x)[/tex]
The derivative of f(x) is equal to (3x - 2)(x^2 - 2x)^2 / (square root(x^2 - 2x)) - 18x(square root(x^2 - 2x)) / (x^2 - 2x).
To find the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule depending on the complexity of the function. In this case, we can use the chain rule to find the derivative of f(x).
The power rule is a method for finding the derivative of a function raised to a power. It states that the derivative of x^n is equal to nx^(n-1). In other words, you bring the power down as a coefficient and subtract 1 from the original power.
The chain rule is used to find the derivative of a composition of functions. In this case, we have a function within a function, so we can use the chain rule by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
Finding the derivative of a function allows us to determine the slope of a tangent line at any point on the function's graph. This can be useful in various applications, such as optimization problems, calculating rates of change, and determining the behavior of a function at critical points.