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:
f(x) = x – 3 sin 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 = `tan x/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 = `sinx/x^2`
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:
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:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
If y = sin–1x then find y”
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 x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
