Logarithmic Differentiation y^x=x^y

Mylo O'Moore

Mylo O'Moore

Answered question

2021-10-09

Logarithmic Differentiation yx=xy

Answer & Explanation

Isma Jimenez

Isma Jimenez

Skilled2021-10-10Added 84 answers

Step 1
Consider the logarithms,
yx=xy
To calculate the derivative (dy/dx) with respect to “x”
Taking log both sides
ln(yx)=ln(xy)
xlny=ylnx   ln(mn)=nln(m)
Now, differentiate the function with respect to “x”
Step 2 ddx(xlny)=ddx(ylnx)
xddxlny+lnyddxx=y1x+lnxddx(y)
x1ydydx+lny=yx+lnxdydx
dydx(xylnx)=yxlny
dydx(xylnxy)=(txlnyx)
dydx=(yxlny)(xylnx)yx
dydx=(yxlny)(xylnx)lnylnx    xlny=ylnx

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