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First, rewrite the function using exponents:f(x) = 3x1/2 - 5x-3/2 (since x√x = x1 * x1/2 = x3/2).Now, find the first derivative f'(x):f'(x) = d/dx (3x1/2 - 5x-3/2)= 3 * (1/2)x-1/2 - 5 * (-3/2)x-5/2= (3/2)x-1/2 + (15/2)x-5/2.Next, find the second derivative f''(x):f''(x) = d/dx ((3/2)x-1/2 + (15/2)x-5/2)= (3/2) * (-1/2)x-3/2 + (15/2) * (-5/2)x-7/2= (-3/4)x-3/2 - (75/4)x-7/2.Convert back to radical form:x-3/2 = 1/(x√x)x-7/2 = 1/(x³√x)So, f''(x) = -3/(4x√x) - 75/(4x³√x).