Use the limit definition to find $f^{\prime }(x)$ for $f(x)=\frac{-6}{x+3}$.

Use the limit definition to find $v^{\prime }(x)$ for $v(x)=\frac{2}{x-5}$.

Use the alternate form $g^{\prime }(a)={\lim }_{x\to a}\frac{g(x)-g(a)}{x-a}$ to find $g^{\prime }(5)$ for $g(x)=x^2+6$.

Use the limit definition to find $q^{\prime }(x)$ for $q(x)=\frac{-1}{x+3}$.

Evaluate ${\lim }_{x\to -2}\frac{x^3+8}{x+2}$ by recognizing it as a derivative.

The limit ${\lim }_{h\to 0}\frac{\sqrt{49+h}-7}{h}$ is the derivative of which function, at which point?

Use the limit definition to find $u^{\prime }(x)$ for $u(x)=\frac{-6}{x+6}$.

Evaluate ${\lim }_{x\to -1}\frac{x^3+1}{x+1}$ by recognizing it as a derivative.

The limit ${\lim }_{h\to 0}\frac{\sqrt{36+h}-6}{h}$ is the derivative of which function, at which point?

Use the definition $q^{\prime }(x)={\lim }_{h\to 0}\frac{q(x+h)-q(x)}{h}$ to find $q^{\prime }(x)$ for $q(x)=-5x^2+x-4$.

The limit ${\lim }_{h\to 0}\frac{\sqrt{169+h}-13}{h}$ is the derivative of which function, at which point?

Use the alternate form $w^{\prime }(a)={\lim }_{x\to a}\frac{w(x)-w(a)}{x-a}$ to find $w^{\prime }(8)$ for $w(x)=x^2+2$.

Use the definition $f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ to find $f^{\prime }(x)$ for $f(x)=6x^2-5x+8$.

Use the limit definition to find $g^{\prime }(x)$ for $g(x)=\frac{-8}{x+2}$.

Use the definition $f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ to find $f^{\prime }(x)$ for $f(x)=x^2+6x-3$.

Evaluate ${\lim }_{x\to 5}\frac{x^3-125}{x-5}$ by recognizing it as a derivative.

The limit ${\lim }_{h\to 0}\frac{\sqrt{121+h}-11}{h}$ is the derivative of which function, at which point?

Use the definition $w^{\prime }(x)={\lim }_{h\to 0}\frac{w(x+h)-w(x)}{h}$ to find $w^{\prime }(x)$ for $w(x)=x^2+5x-1$.

The limit ${\lim }_{h\to 0}\frac{\sqrt{9+h}-3}{h}$ is the derivative of which function, at which point?

Use the definition $p^{\prime }(x)={\lim }_{h\to 0}\frac{p(x+h)-p(x)}{h}$ to find $p^{\prime }(x)$ for $p(x)=6x^2-4x-9$.

Use the limit definition to find $s^{\prime }(x)$ for $s(x)=\frac{-2}{x-1}$.

Use the definition $s^{\prime }(x)={\lim }_{h\to 0}\frac{s(x+h)-s(x)}{h}$ to find $s^{\prime }(x)$ for $s(x)=-4x^2-5x-7$.

The limit ${\lim }_{h\to 0}\frac{\sqrt{196+h}-14}{h}$ is the derivative of which function, at which point?

Use the alternate form $q^{\prime }(a)={\lim }_{x\to a}\frac{q(x)-q(a)}{x-a}$ to find $q^{\prime }(5)$ for $q(x)=x^2+1$.

The limit ${\lim }_{h\to 0}\frac{\sqrt{4+h}-2}{h}$ is the derivative of which function, at which point?

Use the definition $g^{\prime }(x)={\lim }_{h\to 0}\frac{g(x+h)-g(x)}{h}$ to find $g^{\prime }(x)$ for $g(x)=-x^2+8x-3$.

Use the alternate form $p^{\prime }(a)={\lim }_{x\to a}\frac{p(x)-p(a)}{x-a}$ to find $p^{\prime }(-4)$ for $p(x)=x^2+5$.

Use the alternate form $v^{\prime }(a)={\lim }_{x\to a}\frac{v(x)-v(a)}{x-a}$ to find $v^{\prime }(-9)$ for $v(x)=x^2+3$.

Evaluate ${\lim }_{x\to -3}\frac{x^3+27}{x+3}$ by recognizing it as a derivative.

Use the definition $f^{\prime }(x)={\lim }_{h\to 0}\frac{f(x+h)-f(x)}{h}$ to find $f^{\prime }(x)$ for $f(x)=5x^2-4x+4$.