Answer :
The derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵ is given by f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1).
To find the derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵, we can use the chain rule and the power rule of differentiation. Let's proceed step by step:
Step 1: Rewrite the function using the exponentiation notation:
f(x) = √(x⁴ - 3x³ + x)⁵
Step 2: Apply the chain rule by differentiating the outer function with respect to the inner function:
f'(x) = (5/2) × (x⁴ - 3x³ + x[tex])^{\frac{5}{2} - 1 }[/tex]× d/dx (x⁴ - 3x³ + x)
Step 3: Differentiate the inner function, which involves applying the power rule:
f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1)
Therefore, the derivative of the function f(x) = √(x⁴ - 3x³ + x)⁵ is given by f'(x) = (5/2) × √(x⁴ - 3x³ + x)³ × (4x³ - 9x² + 1).
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The complete question is:
Find the derivative of the function f(x)= √(x⁴ − 3x³ + x)⁵
