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Differentiate.......

Algebra
Tutor: None Selected Time limit: 0 Hours

y=(tanx)^(1/x)

Dec 10th, 2014

d(f(x))dx=

ddx((tan(x))1x)

=(tan(x))1xddx(ln(tan(x))1x)

=ddx(ln(tan(x))x)(tan(x))1x

=xddx(ln(tan(x)))ddx(x)ln(tan(x))x2(tan(x))1x

=(tan(x))1x(1tan(x)ddx(tan(x))x−1ln(tan(x)))x2

=(tan(x))1x((sec(x))2xtan(x)−ln(tan(x)))x2

=(tan(x))1x(x(sec(x))2tan(x)−ln(tan(x)))x2

Rewrite/simplify:

=(tan(x))1x((sec(x))2xtan(x)ln(tan(x))x2)


Dec 10th, 2014

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Dec 10th, 2014
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