Advertisements
Advertisements
Question
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` is
Options
`1/27 x^2 (2x^3 + 15)^3`
`2/27 x(2x^3 + 5)^3`
`2/27 x^2(2x^3 + 15)^3`
`- 2/27 x(2x^3 + 5)^3`
Advertisements
Solution
`2/27 x^2(2x^3 + 15)^3`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = (x2 + 5) log(1 + x) e–3x
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 = sin (ex)
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(x)`
Find the derivatives of the following:
xy = yx
Find the derivatives of the following:
(cos x)log x
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
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:
sin-1 (3x – 4x3)
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If y = etan–1x, show that (1 + x2)y” + (2x – 1)y’ = 0
Choose the correct alternative:
If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
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
