Advertisements
Advertisements
प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
उत्तर
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
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:
y = sin x + cos x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Differentiate the following:
y = e–mx
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
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 y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
If f(x) = x tan-1x then f'(1) 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?
