Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = `root(3)(1 + x^3)`
Advertisements
उत्तर
y = `root(3)(1 + x^3)`
y = `(1 + x^3)^(1/3)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = 1/3 (1 + x^3)^(1/3 - 1) xx "d"/("d"x) (1 + x^3)`
`("d"y)/("d"x) = 1/3 (1 + x^3)^(- 2/3) (0 + 3x^2)`
`("d"y)/("d"x) = 1/3 1/(1 + x^3)^(2/3) xx 3x^2`
`("d"y)/("d"x) = x^2/(1 + x^3)^(2/3)`
= `x^2 (1 + x^3)^(- 2/3)`
APPEARS IN
संबंधित प्रश्न
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 = `x/(sin x + cosx)`
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:
y = 4 sec 5x
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = `sqrt(x + sqrt(x + sqrt(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:
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:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
Choose the correct alternative:
`"d"/("d"x) (2/pi sin x^circ)` is
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
Choose the correct alternative:
The number of points in R in which the function f(x) = |x – 1| + |x – 3| + sin x is not differentiable, is
