Advertisements
Advertisements
Question
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Advertisements
Solution
Let y = `cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Put x = `cos 2theta`
`("d"x)/("d"theta) = - sin 2theta xx 2`
`("d"x)/("d"theta) = - 2 sin 2theta` .......(1)
y = `cos[2tan^- sqrt((1 - cos 2theta)/(1 + cos theta))]`
y = `cos[2tan^-1 sqrt((2sin^2theta)/(2cos^2theta))]`
y = `cos[2tan^-1 sqrt(tan^2theta)]`
y = `cos[2tan^-1 (tan theta)]`
y = `cos[2theta]`
`("d"y)/("d"theta) = - sin 2theta xx 2`
`("d"y)/("d"theta) = - 2 sin 2theta` .......(2)
From equation (1) and (2) we get
`(("d"y)/("d"theta))/(("d"x)/("d"theta)) = (- 2sin 2theta)/(- 2 sin 2theta)`
`("d"y)/("d"x)` = 1
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
y = tan 3x
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `(sin^2x)/cos x`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If y = sin–1x then find y”
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` 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
