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`
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:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
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 = `tan x/x`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
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:
y = e-x . log x
Differentiate the following:
y = sin (ex)
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Differentiate the following:
y = sin3x + cos3x
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
tan (x + y) + tan (x – 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:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Choose the correct alternative:
If y = cos (sin x2), then `("d"y)/("d"x)` at x = `sqrt(pi/2)` is
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