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
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = e–mx
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
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"^(xcosx)`
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:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` 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:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
