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350. Assuming that g is a differentiable function, find an expression for the derivative of
351. Assuming that g is a differentiable function, find an expression for the derivative of
Using the Chain Rule to Find Derivatives
352–370 Use the chain rule to find the derivative.
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More Challenging Chain Rule Problems
371–376 Solve the problem related to the chain rule.
371. Find all x values in the interval [0, 2π] where the function
372. Suppose that H is a function such that
373. Let
374. Let
375. Suppose that H is a function such that
376. Let
Chapter 6
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.
The Problems You’ll Work On
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
What to Watch Out For
Although you’re practicing basic formulas for exponential and logarithmic functions, you still use the product rule, quotient rule, and chain rule as before. Here are some tips for solving these problems:
Using logarithmic differentiation requires being familiar with the properties