The derivative function of f(x)=5x⁻²-4x+4 is f'(x)=
-10x⁻³-4
To find the derivative function of f(x), we apply the power rule and the constant multiple rule of differentiation.
Power rule: If f(x)=xⁿ, then f'(x)=nxⁿ⁻¹
Constant multiple rule: If g(x)=cf(x), where c is a constant, then g'(x)=cf'(x)
Using these rules, we can find the derivative of each term separately:
f'(x) = 5(d/dx)x⁻² – 4(d/dx)x + (d/dx)4
Applying the power rule to the first term:
f'(x) = 5(-2x⁻³) – 4(d/dx)x + (d/dx)4
Simplifying the first term:
f'(x) = -10x⁻³ – 4 + 0
Simplifying further:
f'(x) = -10/x³ – 4
Therefore, the derivative function of f(x) is f'(x) = -10/x³ – 4.
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