Advertisements
Advertisements
प्रश्न
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
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 = cosec x . cot x
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 0
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
