Advertisements
Advertisements
Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
Advertisements
Solution
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
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
g(t) = t3 cos t
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x0
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:
y = (x2 + 4x + 6)5
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
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:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
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 = sin–1x then find y”
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) ("e"^(x + 5log x))` is
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:
If x = a sin θ and y = b cos θ, then `("d"^2y)/("d"x^2)` is
