Advertisements
Advertisements
Question
Differentiate the following:
y = `sqrt(x +sqrt(x)`
Advertisements
Solution
y = `sqrt(x +sqrt(x)`
y = `[x + x^(1/2)]^(1/2)`
y = f(g(x))
`("d"y)/("d"x)` = f'(g(x)) . g'(x)
`("d"y)/("d"x) = 1/2 [x + x^(1/2)]^(1/2 - 1) [1 + 1/2 x^(1/2 - 1)]`
`("d"y)/("d"x) = 1/2[x + x^(1/2)]^(- 1/2) [1 + 1/2 x^(- 1/2)]`
= `1/[2x + x^(1/2)]^(1/2) [1 + 1/(2x^(1/2))]`
= `1/(2sqrt(x + sqrt(x))) xx [(2x^(1/2) + 1)/(2x^(1/2))]`
= `1/(2sqrt(x + sqrt(x))) xx [(2sqrt(x) + 1)/(2sqrt(x))]`
`("d"y)/("d"x) = (2sqrt(x) + 1)/(4sqrt(x) * sqrt(x sqrt(x))`
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:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Differentiate the following:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = sin (ex)
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = `x"e"^(-x^2)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = sin2(cos kx)
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = sin–1x then find y”
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:
`"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
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"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
