Advertisements
Advertisements
Question
Differentiate the following:
y = sin3x + cos3x
Advertisements
Solution
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
RELATED QUESTIONS
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) = t3 cos t
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
If y = sin–1x then find y”
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 = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
