Advertisements
Advertisements
प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
उत्तर
y = (x2 + 5) log(1 + x) e–3x
`("d"y)/("d"x) = (x^2 + 5) [log (1 + x)"e"^(-3x) (- 3) + "e"^(-3x) xx 1/(1 + x)] + log(1 + x) * "e"^(-3x) (2x)`
`("d"y)/("d"x) = (x^2 + 5) [- 3"e"^(-3x) log(1 - x) + ("e"^(-3x))/(1 + x)] + 2x "e"^(-3x) log(1 + x)`
`("d"y)/("d"x) = "e"^(-3x) [- 3(x^2 + 5) log(1 + x) + (x^2 + 5)/(1 + x)] + "e"^(-3x) 2x log(1 + x)`
`("d"y)/("d"x) = "e"^(- 3x) [- 3(x^2 + 5) log(1 + x) + (x^2 + 5)/(1 + x) + 2x log (1 + x)`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 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 = cosec x . cot x
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:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = 4 sec 5x
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
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:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
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"`
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 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:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
