Question

Differentiate the following
w.r.t. x :
sin-1 (1 - 2xx)

Answer 1

Answer:

hope help u.................

Answer 2

Answer:

[4x cos(1–2x^2)]/sin^2(1–2x^2)

Step By Step Explaination:

What will be the differentiation of sin^-1 (1-2x^2)?

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To complete this question you must use the chain rule which is dy/dx = dy/du x du/dx Assuming that this question is equal to y.

This is a function within a function so let u = (1–2x^2). du/dx is therefore the differential of u which is (-4x). This is the first part completed.

The second part is dy/du and since y=sin^-1 (u) =(sin u)^-1. Since this section is a function to a power the chain rule needs to be used but I’ll use the short version. The power pops to the front the function is then multiplied by it and the power drops down by one. This is then multiplied by the differential of the bracket. Therefore y=(sin u)^-1 differentiated and therefore dy/du = -1(sin u)^-2 x cos u = -cos u (sin u)^-2.

Since dy/dx = dy/du x du/dx

dy/dx = (-4x)(-cos u(sin u)^-2) = 4x cos u(sin u)^-2 = (4x cos u)/(sin u)^2

Nearly done

Just have to substitute u = (1–2x^2)

Therefore dy/dx = [4x cos(1–2x^2)]/sin^2(1–2x^2) -ANS.