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Chapter 2: Q 29. (page 237)

Fill in the blank:

ddxcotx=---

Short Answer

Expert verified

ddxcotx=-cosec2x

Step by step solution

01

Given Information

The given expression isddxcotx

02

Simplification

Differentiation of cotxis -cosec2x

role="math" localid="1650975118478" 鈬�ddxcotx=-cosec2x

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Most popular questions from this chapter

Use the differentiation rules developed in this section to find

the derivatives of the functions

f(x)=4-x7

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c)for each function f and value x=c in Exercises 23鈥�38.

23.f(x)=x2,x=-3

Use theh鈫�0definition of the derivative to prove the power rule holds for positive integers powers

Taking the limit: We have seen that if f is a smooth function, then f'(c)鈮�f(c+h)-f(c)hThis approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.

f'(c)=limh鈫�0f(c+h)-f(c)h.

Use the limit just defined to calculate the exact slope of the tangent line tof(x)=x2atx=4.

Use the definition of the derivative to prove the following special case of the product rule

ddx(x2f(x))=2xf(x)+x2f'(x)
See all solutions

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