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Differentiate the following w.r.t. x. ...

Differentiate the following w.r.t. x.
a. `tan^3x` b. `tanx^2` c. `sin^2sqrtx`

Text Solution

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a. Let `y=tan^3x=(tanx)^3`, `(dy)/(dx)=3(tan^2x)(sec^2x)`
b. Let `y=tan(x^2)`, `(dy)/(dx)=sec^2(x^2)2x`
c. Let `y=sin^2(sqrtx)=(sinsqrtx)^2`
`(dy)/(dx)=2(sinsqrtx)cos(sqrtx)1/2x^(-1//2)=(1)/(2sqrtx)sin(2sqrtx)`
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