Advertisements
Advertisements
Question
Find the derivatives of the following:
sin-1 (3x – 4x3)
Advertisements
Solution
Let y = sin–1 (3x – 4x3)
Put x = sin θ
y = sin–1 (3 sin θ – 4 sin3 θ)
y = sin–1 (sin 3θ)
y = 3θ
y = 3 sin–1x
`("d"y)/("d"x) = 3/sqrt(1 - x^2)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
