Advertisements
Advertisements
Question
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Solution
y = `"e"^(3x)/(1 + "e"^x`
`("d"y)/("d"x) = ((1 + "e"^x) "e"^(3x) (3) - "e"^(3x) (0 + "e"^x))/(1 + "e"^x)^2`
`("d"y)/("d"x) = (3(1 + "e"^x) "e"^(3x) - "e"^(3x) * "e"^x)/(1 + "e"^x)^2`
`("d"y)/("d"x) = (3"e"^(3x) + 3"e"^x "e"^(3x) - "e"^x "e"^(3x))/(1 + "e"^x)^2`
= `(3"e"^(3x) + 2"e"^x "e"^(3x))/(1 + "e"^x)^2`
= `(3"e"^(3x) + 2"e"^(x + 3x))/(1 + "e"^x)^2`
`("d"y)/("d"x) = (3"e"^(3x) + 2"e"^(4x))/(1 + "e"^x)^2`
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:
y = `(tanx - 1)/secx`
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 = x sin x cos 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:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Find the derivatives of the following:
y = `x^(cosx)`
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = `"a" cos^3"t"` ; y = `"a" sin^3"t"`
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:
`cos^-1 ((1 - x^2)/(1 + x^2))`
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 f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at 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
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
