Answer :
The derivative of the function y = [tex]x^{-9}+x^{-6}+x^{-1}[/tex] is given by y' = [tex]-9x^{-10}-6x^{-7}-\ln x[/tex] and the derivative of the function y = 9x⁵ - 4x³ + 5x - 8 is given by 45x⁴ - 12x² +5.
The function given is,
y = [tex]x^{-9}+x^{-6}+x^{-1}[/tex]
In the above function, independent variable is 'x' and dependent variable is 'y'.
Differentiating the above function with respect to 'x' we get,
dy/dx = d/dx [tex](x^{-9}+x^{-6}+x^{-1})[/tex]
y'(x) = [tex]-9x^{-9-1}-6x^{-6-1}-\ln x=-9x^{-10}-6x^{-7}-\ln x[/tex]
Another function is,
y = 9x⁵ - 4x³ + 5x - 8
Differentiating the above function with respect to 'x' we get,
y' = 9*5x⁴ - 4*3x² + 5 - 0 = 45x⁴ - 12x² +5
Hence the derivative functions are [tex]-9x^{-10}-6x^{-7}-\ln x[/tex] and 45x⁴ - 12x² +5.
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