Advertisements
Advertisements
Question
Differentiate the following with respect to x.
sin2 x
Advertisements
Solution
For the following problems chain rule to be used:
`"d"/"dx"` f(g(x)) = f'(g(x)) . g'(x)
`"d"/"dx"` [f(x)]n = n[f(x)]n-1 × `"d"/"dx"`f(x)
Let y = sin2 x = (sin x)2
`"dy"/"dx" = 2(sin x)^(2-1) "d"/"dx" (sin x)`
= 2 sin x (cos x)
= sin 2x
APPEARS IN
RELATED QUESTIONS
Differentiate the following with respect to x.
x3 ex
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
x sin x
Differentiate the following with respect to x.
`sqrt(1 + x^2)`
If 4x + 3y = log(4x – 3y), then find `"dy"/"dx"`
Differentiate the following with respect to x.
(sin x)tan x
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Differentiate sin2x with respect to x2.
If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x2) y2 + xy1 – m2y = 0
