Find the derivative of the function by the limit process


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Find the derivative of the following function using the limit process

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\displaystyle
f'(x)=\lim_{\Delta x\to 0}\dfrac{-3(x+\Delta x)^2-9(x+\Delta x)-(-3x^2-9x)}{\Delta x}\\
f'(x)=\lim_{\Delta x\to 0}\dfrac{-3x^2-6x\Delta x-3(\Delta x)^2-9x-9\Delta x+3x^2+9x}{\Delta x}\\
f'(x)=\lim_{\Delta x\to 0}\dfrac{-6x\Delta x-3(\Delta x)^2-9\Delta x}{\Delta x}\\
f'(x)=\lim_{\Delta x\to 0}\dfrac{\Delta x(-6x-3x\Delta x-9)}{\Delta x}\\
f'(x)=\lim_{\Delta x\to 0}(-6x-3x\Delta x-9)\\
f'(x)=-6x-3x\cdot 0-9\\
f'(x)=-6x-9\Rightarrow \text{C}




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