Advertisements
Advertisements
प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
Advertisements
उत्तर
y = ex sin x
⇒ y = uv’ + vu’
Now u = ex
⇒ u’ = `("d"u)/("d"x) "e"^x`
v = sin x
⇒ v’ = `("d"v)/("d"x)` cos x
i.e. y’ = ex (cos x) + sin x (ex)
= ex [sin x + cos x]
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos x
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:
y = `tan x/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 = `x/(sin x + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
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 = (x2 + 5) log(1 + x) e–3x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = tan 3x
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = cos (a3 + x3)
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`x^2/"a"^2 + y^2/"b"^2` = 1
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
