Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `x"e"^(-x^2)`
Advertisements
उत्तर
y = `x"e"^(-x^2)`
y = uv where u = x and v = `"e"^(-x^2)`
Now u’ = 1 and v’ = `"e"^(-x^2) (- 2x)`
v’ = `- 2x"e"^(-x^2)`
Now y = uv
⇒ y’ = uv’ + vu’
(i..e.) `("d"y)/("d"x) = x[- 2x"e"^(-x^2)] + "e"^(-x^2) (1)`
= `"e"^(- x^2) (1 - 2x^2)`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = ex sin x
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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = e-x . log x
Differentiate the following:
y = (x2 + 4x + 6)5
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
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
