Evaluate the following derivatives. \frac{d}{dx}(x^{\tan x})

Russell Gillen

Russell Gillen

Answered question

2022-01-17

Evaluate the following derivatives.
ddx(xtanx)

Answer & Explanation

poleglit3

poleglit3

Beginner2022-01-18Added 32 answers

Step 1
Given:
Let y=xtanx
Taking \ln on both sides
lny=lnxtanx
We know that lnam=mlna
lny=(tanx)lnx
Step 2
Differentiating on both sides
1ydydx=tanx(1x)+sec2x(lnx)
dydx=y(tanxx+lnx(sec2x))
dydx=xtanx(tanxx+lnx(sec2x))
dydx=xtanx1tanx+xtanxlnx(sec2x)
Hence the derivative of xtanx1tanx+xtanxlnx(sec2x)

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