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Given $f(x)=2-5x^2,$ using the limit definition of derivative, find $f^{\text{'}}(x).$

$(15$ points$)$ Find $f^{\text{'}}(x)$ for the following:

a$)f(x)=-11x^2-14x+{}^6-8e^x$

$6$a$)$

b$)f(x)=\frac{x^4}{8}$

$6$b$)$

c$)f(x)=-6\sqrt[3]{x^2}$

$6$c$)$