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# Find the derivative of the function using the definition of derivative. g(x) = 9 - x

**Solution:**

It is given that

g(x) = 9 - x

The derivative of the given function is

\(\\g'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} \\ \\Substituting\: the \: values \\ \\g'(x)=\lim_{h\rightarrow 0}\frac{[5-(x+h)]-[5-x]}{h} \\ \\g'(x)=\lim_{h\rightarrow 0}\frac{5-x-h-5+x}{h} \\ \\By\: further\: calculation\)

\(\\g'(x)=\lim_{h\rightarrow 0}\frac{-h}{h} \\ \\g'(x)=\lim_{h\rightarrow 0}-1\)

g’(x) = -1

Therefore, the derivative of the function is -1.

## Find the derivative of the function using the definition of derivative. g(x) = 9 - x

**Summary:**

The derivative of the function using the definition of derivative g(x) = 9 - x is -1.

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