Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Advertisements
उत्तर
y = `sin(tan(sqrt(sinx)))`
y = f(g(x))
`("d"y)/("d"x)` = f'(g(x)) . g'(x)
`("d"y)/("d"x) = cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) xx 1/2(sinx)^(1/2 - 1) cos x`
`("d"y)/("d"x) = 1/2 cos (tan(sqrt(sinx))) sec^2 (sqrt(sinx)) (sinx)^(- 1/2) cosx`
`("d"y)/("d"x) = (cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) cosx)/(2(sinx)^(1/2)`
APPEARS IN
संबंधित प्रश्न
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:
g(t) = 4 sec t + tan t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `x/(sin x + cosx)`
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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = `x"e"^(-x^2)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
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 f(x) = x tan-1x then f'(1) is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
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 y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
