Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Advertisements
Solution
y = `sinx/(1 + cosx)`
= `u/v` ....(say)
u = sin x v = 1 + cos x
u’ = cos x v’ = – sin x
y = `u/v`
⇒ y' = `(vu"'" - uv"'")/v^2`
(i.e.,) `("d"y)/("d"x) = ((1 + cosx) cosx - sin(0 - sinx))/(1 + cosx)^2`
`("d"y)/("d"x) = (cosx + cos^2 x - sin^2x)/(1 + cosx)^2`
`("d"y)/("d"x) = (1 + cos x)/(1 + cosx)^2`
= `1/(1 + cosx)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
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:
F(x) = (x3 + 4x)7
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
sin-1 (3x – 4x3)
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 x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Find the derivatives of the following:
If sin y = x sin(a + y), the prove that `("d"y)/("d"x) = (sin^2("a" + y))/sin"a"`, a ≠ nπ
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:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log 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
