Differentiate the following implicit
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Take log on both sides
Log(x^y. y^x) =log16
Log(x^y) +log(y^x) =log16
ylogx+xlogy=log16
Diff. w.r.to. x
y/x+(logx)y'+(x/y)y'+logy=0
y'(logx+x/y)=-(logy+y/x)
y'(ylogx+x)/y=-(xlogy+y)/x
y'=-x{(logy^x)+y}÷y{(logx^y)+x}
Log(x^y. y^x) =log16
Log(x^y) +log(y^x) =log16
ylogx+xlogy=log16
Diff. w.r.to. x
y/x+(logx)y'+(x/y)y'+logy=0
y'(logx+x/y)=-(logy+y/x)
y'(ylogx+x)/y=-(xlogy+y)/x
y'=-x{(logy^x)+y}÷y{(logx^y)+x}
anunaysharma:
Did you apply product rule in step 4?
yes
is it helpful
yes thank you so much
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