Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `(sin^2x)/cos x`
Advertisements
उत्तर
y = `(sin^2x)/cos x`
`("d"y)/("d"x) = (cosx(2sinx cos x) - sin^2x xx - sin x)/(cos x)^2`
`("d"y)/("d"x) = (2sinx cos^2x + sin^3x)/(cos^2x)`
= `sin x ((2 cos^2 x + sin^2 x))/(cos^2x)`
= `sin x((2cos2x)/(cos^2x) + (sin2x)/(cos2x))`
= sin x(2 + tan2x)
= sin x(1 + 1 + tan2x)
`("d"y)/("d"x)` = sin x(1 + sec2 x)
APPEARS IN
संबंधित प्रश्न
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 = x sin x cos x
Differentiate the following:
y = sin (ex)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = e–mx
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
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
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` 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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)` then `("d"y)/("d"x)` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
