Advertisements
Advertisements
प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
Advertisements
उत्तर
y = `x/(sin x + cosx)`
`("d"y)/("d"x) = ((sinx + cosx)(1) - x(cosx - sinx))/(sinx + cos x)^2`
`("d"y)/("d"x) = ((sinx + cosx)- x(cosx - sinx))/(sinx + cos x)^2`
`("d"y)/("d"x) = (sinx + cosx - xcosx + xsinx)/(sinx + cosx)^2`
`("d"y)/("d"x) = ((1 + x) sinx + (1 - x)cosx)/(sinx + cosx)^2`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
sin-1 (3x – 4x3)
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 y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
