Q. 165.0( 1 Vote )

Differentiate <sp

Answer :

Let u = cos–1(4x3 – 3x) and


We need to differentiate u with respect to v that is find.


We have u = cos–1(4x3 – 3x)


By substituting x = cos θ, we have


u = cos–1(4cos3θ – 3cosθ)


But, cos3θ = 4cos3θ – 3cosθ


u = cos–1(cos3θ)


Given,


However, x = cos θ





Hence, u = cos–1(cos3θ) = 3θ


u = 3cos–1x


On differentiating u with respect to x, we get




We know




Now, we have


By substituting x = cos θ, we have




[ sin2θ + cos2θ = 1]



v = tan–1(tanθ)


However,


Hence, v = tan–1(tanθ) = θ


v = cos–1x


On differentiating v with respect to x, we get



We know



We have





Thus,


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