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Chapter 2: Q. 85 (page 235)

Use the quotient rule and the derivative of the sine function to prove that ddx(csx)=-cscx.cotx

Short Answer

Expert verified

The function ddx(csx)=-cscx.cotxhas been proved.

Step by step solution

01

Step 1. Given Information.

The function:

ddx(csx)=-cscx.cotx

02

Step 2. Quotient rule.

The quotient rule is:

(fg)'(x)=f'(x)g(x)-g'(x)f(x)(g(x))2

03

Step 3. Obtain the derivative for the given function.

f'(cscx)=f'(1sinx)=1'(sinx)-1(sinx)'(sinx)2=-cosxsin2x=-1sinx.cosxsinx=-csc.cotx

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Most popular questions from this chapter

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

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Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=(3x+1)3,f(2)=1
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