Find the derivative by the limit process. \

$$f(x)=3$$

Find the derivative by the limit process.

$$f(x)=x^3-12x$$

Find the derivative by the limit process.

$$f(x)=\sqrt{x+4}$$

Find the derivative by the limit process.

ƒ(x) = 1 - x²

Find the derivative by the limit process. $f(x)=8-\frac{1}{5} x$

Find the derivative by the limit process.

f(x) = 3x + 2

Find the derivative by the limit process.

f(x) = -10x

Consider the linear function $y=a x+b$. If $x$ changes at a constant rate, does $y$ change at a constant rate? If so, does it change at the same rate as $x$ ? Explain.

Find the derivative of the function. \

$$f(x)=\left(9-x^2\right)^{2 / 3}$$

Find the derivative of the function. \

$$f(x)=6 x-5 e^x$$

Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than $0.001$. Then find the zero(s) using a graphing utility and compare the results. \

$$f(x)=x+\sin (x+1)$$

Find $d y / d x$ by implicit differentiation. \

$$x^3-2 x^2 y+3 x y^2=38$$

Use the Quotient Rule to differentiate the function. \

$$g(x)=\dfrac{\sin x}{x^2}$$

Find $d y / d x$ at the indicated point for the equation. \

$$x=y^3-7 y^2+2,(-4,1) \quad$$