Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Advertisements
Solution
y = e-x logx = uv (say)
Here u = e-x and v = log x
⇒ u’ = -e-x and v’ = `1/x`
Now y = uv
⇒ y’ = uv’ + vu’
(i.e.) `("d"y)/("d"x) = "e"^-x (1/x) + log x(-"e"^-x)`
`("d"y)/("d"x) = "e"^-x (1/x - log x)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = 4 sec t + tan t
Differentiate the following:
y = tan 3x
Differentiate the following:
y = sin (ex)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `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:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log 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
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
