Advertisements
Advertisements
Question
If y = sec (tan−1x), then `dy/dx` at x = 1 is ______.
Options
`1/2`
1
`1/sqrt(2)`
`sqrt(2)`
Advertisements
Solution
If y = sec (tan−1x), then `dy/dx` at x = 1 is `underlinebb(1/sqrt(2))`.
Explanation:
[Hint: `dy/dx = sec(tan^-1x).tan(tan^-1x) xx (1)/(1 + x^2)`
∴ `(dy/dx)_("at" x = 1) = sec(tan^-1 1) xx 1 xx (1)/(1 + 1^2)`
= `sec π/4 xx (1)/(2) = sqrt(2) xx (1)/(2) = (1)/sqrt(2).]`
APPEARS IN
RELATED QUESTIONS
If y = eax. cos bx, then prove that
`(d^2y)/(dx^2) - 2ady/dx + (a^2 + b^2)y` = 0
Solve the following differential equation:
x2 dy + (xy + y2) dx = 0, when x = 1 and y = 1
Find `dy/dx`, if `xsqrt(x) + ysqrt(y) = asqrt(a)`.
Find `dy/dx if x + sqrt(xy) + y = 1`
Find the second order derivatives of the following : e2x . tan x
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = (5x3 - 4x2 - 8x)9
Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`
Choose the correct alternative.
If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
Fill in the Blank.
If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`.
Find `"dy"/"dx"`, if y = xx.
If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______
Choose the correct alternative:
If y = `root(3)((3x^2 + 8x - 6)^5`, then `("d"y)/("d"x)` = ?
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If x2 + y2 = a2, then `("d"y)/("d"x)` = = 2x + 2y = 2a
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If y = `sin^-1 {xsqrt(1 - x) - sqrt(x) sqrt(1 - x^2)}` and 0 < x < 1, then find `("d"y)/(dx)`
If f(x) = |cos x|, find f'`((3pi)/4)`
Differentiate the function from over no 15 to 20 sin (x2 + 5)
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if ,
`x= e^(3t) , y = e^(4t+5)`
If f(x) = `sqrt(7*g(x) - 3)`, g(3) = 4 and g'(3) = 5, find f'(3).
If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.
If y = f(u) is a differentiable function of u and u = g(x) is a differentiate function of x such that the composite function y = f[g(x)] is a differentiable function of x then prove that
`dy/dx = dy/(du) xx (du)/dx`
Hence find `dy/dx` if y = log(x2 + 5)
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following:
If y = `root(5)((3"x"^2 + 8"x" + 5)^4)`, find `"dy"/"dx"`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
