Question - Derivative Calculation for a Function
Solution:
The function f(x) provided in the image is:f(x) = (3x^5 - x^5) / 18xTo differentiate this function, let's first simplify the expression f(x) by combining like terms in the numerator:f(x) = (3x^5 - x^5) / 18x = (2x^5) / 18x = (1/9)x^4Now that we have the simplified form of f(x), we can differentiate it with respect to x:f'(x) = d/dx [(1/9)x^4] = (1/9) * d/dx [x^4] = (1/9) * (4x^3)Therefore, f'(x) = (4/9)x^3Hence, the derivative of the function f(x) is (4/9)x^3 and is differentiable everywhere except at x = 0, since the original function included a term in the denominator with x, which would not be defined for x = 0.
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