Question

Section 3.1 The Derivative and the Tangent Line Problem
Homework Assignment

   Find the derivative of the function by the limit process

   f(x)=1/x^2
   h(s)=-2√s

   Find the equation of the tangent line to the graph of the function at the given point.

   f(x)=x^3+1,(-1,0)
   f(x)=x-1/x,(1,0)

Section 3.2 Basic Differentiation Rules and Rates of Change
Homework Assignment
   Find the derivative of the function

   g(x)=∜x
   y=2x^3+6x^2-1
   g(t)=π cos⁡t
   y=7x^4+2 sin⁡x
   y=3/4 e^x+2 cos⁡x
   h(x)=(4x^3+2x+5)/x
   y=x^2 (2x^2-3x)
   y=3/〖(2x)〗^3 +2 sin⁡x
   g(x)=√x-3e^x
   Find the equation of the tangent line to the graph of the function f(x)=2/∜(x^3 ) at the point (1, 2).
Section 3.3 Product and Quotient Rules and Higher-Order Derivatives
Homework Assignment
   Find the derivative of the function

   g(s)=√s(s^2+8)
   g(x)=√x sin⁡x
   f(x)=x^2/(2√x+1)
   f(t)=cos⁡t/t^3
   y=sec⁡x/x
   f(x)=sin⁡x cos⁡x
   y=(2e^x)/(x^2+1)


   Find equation of the tangent line to the graph of the function f(x)=(x+3)/(x-3) at the point (4, 7)

Answer 1

Section 3.1 , function is differentiated using first principle.

equation of tangent is (y-y1)=m(x-x1)