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:
g(t) = t3 cos t
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 = `sinx/(1 + cosx)`
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 = cosec x . cot x
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin2(cos kx)
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:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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:
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
