Advertisements
Advertisements
Question
Differentiate the following:
y = (x2 + 4x + 6)5
Solution
Let = u = x2 + 4x + 6
⇒ `("d"u)/("d"x)` = 2x + 4
Now y = u5
⇒ `("d"y)/("d"x)` = 5u4
∴ `("d"y)/("d"x) = ("d"y)/("d"x) xx ("d"u)/("d"x)` = 5u4 (2x + 4)
= 5(x2 + 4x + 6)4 (2x + 4)
= 5(2x + 4) (x2 + 4x + 6)4
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = sin x + cos 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 = tan θ (sin θ + cos θ)
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos x
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = e–mx
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Differentiate the following:
y = `"e"^(xcosx)`
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:
(cos x)log x
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
If y = `1/4 u^4`, u = `2/3 x^3 + 5`, then `("d"y)/("d"x)` 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 differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If f(x) = `{{:("a"x^2 - "b"",", - 1 < x < 1),(1/|x|",", "elsewhere"):}` is differentiable at x = 1, then
