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Use logarithmic differentiation to find the derivative of given function

f(x)=(sinx)cosx

Short Answer

Expert verified

The derivative of given function is

f(x)=sinxln(sinx)+cos2xsinx(sinx)cosx

Step by step solution

01

Step 1.Given data 

We have been given a function to find the derivative for them

f(x)=(sinx)cosx

02

Step 2.Taking log on both side to get the differentiation 

f(x)=(sinx)cosxlnf(x)=ln(sinx)cosx[Taking log in both sides]lnf(x)=cosxln(sinx)f(x)f(x)=ddx(cosxln(sinx))Differentiate both sideswith respect toxf(x)f(x)=ddx(cosx)ln(sinx)+cosxddxln(sinx)

=sinxln(sinx)+cosxsinxddxsinx=sinxln(sinx)+cosxsinx(cosx)

Using product rule and chain rule

f(x)=sinxln(sinx)+cosxsinx(cosx)f(x)

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