Advertisements
Advertisements
Question
If f(x) = x + 1, find `d/dx (fof) (x)`
Advertisements
Solution
Given:
`f (x) = x + 1`
`fof (x) = (x + 1) + 1 = x + 2`
`d/dx (fof) (x) = d/dx (x + 2) = 1`.
RELATED QUESTIONS
Differentiate the function with respect to x.
sin (x2 + 5)
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
Discuss the continuity and differentiability of the
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
| COLUMN-I | COLUMN-II |
| (A) If a function f(x) = `{((sin3x)/x, "if" x = 0),("k"/2",", "if" x = 0):}` is continuous at x = 0, then k is equal to |
(a) |x| |
| (B) Every continuous function is differentiable | (b) True |
| (C) An example of a function which is continuous everywhere but not differentiable at exactly one point |
(c) 6 |
| (D) The identity function i.e. f (x) = x ∀ ∈x R is a continuous function |
(d) False |
|sinx| is a differentiable function for every value of x.
Show that the function f(x) = |sin x + cos x| is continuous at x = π.
sinx2 + sin2x + sin2(x2)
`sin^-1 1/sqrt(x + 1)`
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
The differential coefficient of `"tan"^-1 ((sqrt(1 + "x") - sqrt (1 - "x"))/(sqrt (1+ "x") + sqrt (1 - "x")))` is ____________.
If `"f"("x") = ("sin" ("e"^("x"-2) - 1))/("log" ("x" - 1)), "x" ne 2 and "f" ("x") = "k"` for x = 2, then value of k for which f is continuous is ____________.
If sin y = x sin (a + y), then value of dy/dx is
If f(x) = `{{:(ax + b; 0 < x ≤ 1),(2x^2 - x; 1 < x < 2):}` is a differentiable function in (0, 2), then find the values of a and b.
The function f(x) = x | x |, x ∈ R is differentiable ______.
The set of all points where the function f(x) = x + |x| is differentiable, is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
For \[v\ne0\], what is the derivative of \[\frac{u}{v}\]?
What is \[\frac{d}{dx}(x^n)\]?
What is \[\frac{d}{dx}(\cos x)\]?
Which limit is the right-hand derivative at \[x=c\]?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[a\]?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[b\]?
If \[f\] is differentiable at \[c\], which limit equals \[f'(c)\]?
For \[x\ne c\], which identity is used to prove that differentiability implies continuity?
Why is \[|x|\] not differentiable at \[x=0\]?
