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:
f(x) = x sin x
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 = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
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:
If f(x) = x tan-1x then f'(1) 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?
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
