Calculus Essentials For Dummies

Chapter 4

Differentiation Orientation

IN THIS CHAPTER

Discovering the simple algebra behind the calculus

Finding the derivatives of lines and curves

Tackling the tangent line problem and the difference quotient

Differential calculus is the mathematics of change and of infinitesimals. You might say it’s the mathematics of infinitesimal changes — changes that occur every gazillionth of a second.

Without differential calculus — if you’ve got only algebra, geometry, and trigonometry — you’re limited to the mathematics of things that either don’t change or that change or move at an unchanging rate. Remember those problems from algebra? One train leaves the station at 3 p.m. going west at 80 mph. Two hours later another train leaves going east at 50 mph… . You can handle such a problem with algebra because the speeds or rates are unchanging. Our world, however, isn’t one of unchanging rates — rates are in constant flux.

Think about putting men on the moon. Apollo 11 took off from a moving launch pad (the earth is both rotating on its axis and revolving around the sun). As the Apollo flew higher and higher, the friction caused by the atmosphere and the effect of the earth’s gravity were ...