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Chapter 2: Q. 84 (page 235)

Use the quotient rule and the derivative of the cosine function to prove that ddx(secx)=secx.tanx

Short Answer

Expert verified

The derivative ddx(secx)=secx.tanx has been proved.

Step by step solution

01

Step 1. Given Information.

The function:

ddx(secx)=secx.tanx

02

Step 2. Quotient rule.

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

03

Step 3. Use the quotient rule on the function.

f'(secx)=f'(1cosx)=(1)'(cosx)-1(cosx)'(cosx)2=-(-sinx)cos2x=1cosx.sinxcosx=secx.tanx

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