Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = sin3x + cos3x
Advertisements
उत्तर
y = sin3x + cos3x
Here u = sin3x = (sin x)3
⇒ `("d"u)/("d"x)` = 3(sin x)2(cos x)
= 3sin2x cosx
v = cos3x = (cos x)3
⇒ `("d"u)/("d"x)` = 3(cos x)2 (– sin x)
= – 3 sin x cos2x
Now y = u + v
⇒ `("d"y)/("d"x) = ("d"u)/("d"x) + ("d"v)/("d"x)`
= 3 sin2x cos x – 3sin x cos2x
= 3 sin x cos x (sin x – cos x)
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan 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 = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
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"`
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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
