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Differentiate t2=tan⁡xt^2= \tan x

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Full solution

Q. Differentiate t2=tan⁡xt^2= \tan x
  1. Differentiate t2t^2: Differentiate t2t^2 with respect to tt.d(t2)dt=2t\frac{d(t^2)}{dt} = 2t
  2. Differentiate tan⁡(x)\tan(x): Differentiate tan⁡(x)\tan(x) with respect to xx.d(tan⁡(x))dx=sec⁡2(x)\frac{d(\tan(x))}{dx} = \sec^2(x)
  3. Set equal and solve: Set the derivatives equal to each other since t2=tan⁡(x)t^2 = \tan(x). \newline2t=sec⁡2(x)2t = \sec^2(x)

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