Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
Чтение книги онлайн.

Читать онлайн книгу Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) - Patrick Jones страница 25

Название: Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice)

Автор: Patrick Jones

Издательство: John Wiley & Sons Limited

Жанр: Математика

Серия:

isbn: 9781119883678

isbn:

СКАЧАТЬ

      351. Assuming that g is a differentiable function, find an expression for the derivative of math.

       352–370 Use the chain rule to find the derivative.

      352. math

      353. math

      354. math

      355. math

      356. math

      357. math

      358. math

      359. math

      360. math

      361. math

      362. math

      364. math

      365. math

      366. math

      367. math, where math

      368. math

      369. math

      370. math

      371–376 Solve the problem related to the chain rule.

      371. Find all x values in the interval [0, 2π] where the function math has a horizontal tangent line.

      372. Suppose that H is a function such that math for math. Find an expression for the derivative of math.

      373. Let math, math, math, math, and math. Find the value of F'(2).

      374. Let math, math, math, and math. Find the value of F'(2).

      375. Suppose that H is a function such that math for math. Find an expression for the derivative of math.

      376. Let math, math, math, math, and math. Find the value of F'(4).

      Exponential and Logarithmic Functions and Tangent Lines

      After becoming familiar with the derivative techniques of the power, product, quotient, and chain rules, you simply need to know basic formulas for different functions. In this chapter, you see the derivative formulas for exponential and logarithmic functions. Knowing the derivative formulas for logarithmic functions also makes it possible to use logarithmic differentiation to find derivatives.

      In many examples and applications, finding either the tangent line or the normal line to a function at a point is desirable. This chapter arms you with all the derivative techniques, so you’ll be in a position to find tangent lines and normal lines for many functions.

      In this chapter, you do the following types of problems:

       Finding derivatives of exponential and logarithmic functions with a variety of bases

       Using logarithmic differentiation to find a derivative

       Finding the tangent line or normal line at a point

      Although you’re practicing basic formulas for exponential and logarithmic functions, СКАЧАТЬ