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:
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 = x sin x cos 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:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = cos (a3 + x3)
Differentiate the following:
y = e–mx
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(xcosx)`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
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:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Choose the correct alternative:
If y = `1/("a" - z)`, then `("d"z)/("d"y)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
