Advertisements
Advertisements
प्रश्न
Differentiate the following:
F(x) = (x3 + 4x)7
Advertisements
उत्तर
F(x) = (x3 + 4x)7
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
F'(x) = `7(x^3 + 4x)^(7 - 1) "d"/("d"x) (x^3 + 4x)`
= 7(x3 + 4x)6 (3x2 + 4)
= 7(3x2 + 4)(x3 + 4x)6
APPEARS IN
संबंधित प्रश्न
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:
y = log10 x
Differentiate the following:
y = `root(3)(1 + x^3)`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = sin2(cos kx)
Differentiate the following:
y = `"e"^(xcosx)`
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:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
Find the derivatives of the following:
If y = `(cos^-1 x)^2`, prove that `(1 - x^2) ("d"^2y)/("d"x)^2 - x ("d"y)/("d"x) - 2` = 0. Hence find y2 when x = 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:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
