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if y = sin^(-1)[(6x-4sqrt(1-4x^2))/5] Find dy/dx. - CBSE (Commerce) Class 12 - Mathematics

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Question

if `y = sin^(-1)[(6x-4sqrt(1-4x^2))/5]` Find `dy/dx `.

Solution

Given that

`y = sin^(-1)[(6x-4sqrt(1-4x^2))/5]`

if y = sin-1x, then `dy/dx=1/sqrt(1-x^2)`

`y = sin^(-1)[6x-4sqrt(1-4x^2)/5]`

`=> y = sin^(-1)[(6x)/5-(4sqrt(1-4x^2))/5]`

`=> y =sin^(-1)[(2x xx3)/5-(4sqrt(1-(2x)^2))/5]`

`=>y = sin^(-1)[2xx3/5-4/5sqrt(1-(2x)^2)]`

`=>y = sin^(-1)[2xxsqrt(1-(4/5)^2)-4/5sqrt(1-(2x)^2)]`

We know that

`sin^(-1)p-sin^(-1)q=sin^-1(psqrt(1-q^2)-qsqrt(1-p^2)))`

Here, p=2x and  `q=4/5`

Therefore,

`y= sin^(-1)2x-sin^(-1)`

Differentiating the above function with respect to x, we have,

 `dy/dx=1/sqrt(1-(2x)^2)xx2-0`

 `=>dy/dx=2/sqrt(1-4x^2)`

  Is there an error in this question or solution?

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Solution if y = sin^(-1)[(6x-4sqrt(1-4x^2))/5] Find dy/dx. Concept: Derivatives of Inverse Trigonometric Functions.
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