Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `"e"^sqrt(x)`
Advertisements
उत्तर
y = `"e"^sqrt(x)`
y = `"e"^(x 1/2)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = "e"^(x 1/2) xx "d"/("d"x) (x^(1/2))`
`("d"y)/("d"x) = "e"^sqrt(x) xx 1/2 xx x^(- 1/2)`
`("d"y)/("d"x) = 1/2 "e"^sqrt(x) xx 1/sqrt(x)`
`("d"y)/("d"x) = 1/(2sqrt(x)) "e"^sqrt(x)`
APPEARS IN
संबंधित प्रश्न
Differentiate the following:
y = tan 3x
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `"e"^(xcosx)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
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:
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 y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a 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 x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
