The derivative of f(x) = negative 10 divided by x at x = -12 is 5 divided by 6, the correct option is D.
What is the differentiation?
Differentiation, in mathematics, process of finding the derivative, or rate of change, of a function.
The given function is;
[tex]\rm f(x)=\dfrac{-10}{x}[/tex] at x = -12.
Differentiation of the function with respect to x
[tex]\rm f(x)=\dfrac{-10}{x}\\\\\rm f'(x)= -10 \times x^{-1}\\\\f'(x)= -10 \times (-1) \times x^{-1-1} \times x\\\\\f'(x)= 10 \times x^{-2}\\\\ f'(x)= \dfrac{10}{x^2} \times x\\\\x = -12\\\\f'(x)= \dfrac{10 \times 12}{(12)^2}\\\\ f'(x)=\dfrac{10 \times -12}{-144}\\\\ f'(x)=\dfrac{5}{6}[/tex]
Hence, the derivative of f(x) = negative 10 divided by x at x = -12 is 5 divided by 6, the correct option is D.
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