Advertisements
Advertisements
Question
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Advertisements
Solution
Let, y = `(sin (ax + b))/(cos (cx + d))`
On differentiating with respect to x,
`dy/dx = d/dx (sin(ax + b)/cos(cx + d))`
= `(cos (cx + d) d/dx sin (ax + b) - sin (ax + b)d/dx cos (cx + d))/cos^2 (cx + d)`
= `(a cos (cx + d)cos (ax + b) + c sin (ax + b)sin (cx + d))/cos^2(cx + d)`
= a cos (ax + b) sec (cx + d) + c sin (ax + b) tan (cx + d) sec (cx + d)
APPEARS IN
RELATED QUESTIONS
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Differentiate the function with respect to x:
(3x2 – 9x + 5)9
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
If f(x) = x + 1, find `d/dx (fof) (x)`
If y = tan(x + y), find `("d"y)/("d"x)`
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Let f(x)= |cosx|. Then, ______.
| 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 |
cos |x| is differentiable everywhere.
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
`tan^-1 (("a"cosx - "b"sinx)/("b"cosx - "a"sinx)), - pi/2 < x < pi/2` and `"a"/"b" tan x > -1`
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
If sin y = x sin (a + y), then value of dy/dx is
Let c, k ∈ R. If f(x) = (c + 1)x2 + (1 – c2)x + 2k and f(x + y) = f(x) + f(y) – xy, for all x, y ∈ R, then the value of |2(f(1) + f(2) + f(3) + ... + f(20))| is equal to ______.
Let f: R→R and f be a differentiable function such that f(x + 2y) = f(x) + 4f(y) + 2y(2x – 1) ∀ x, y ∈ R and f’(0) = 1, then f(3) + f’(3) is ______.
The function f(x) = x | x |, x ∈ R is differentiable ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
What is \[\frac{d}{dx}(x^n)\]?
Which limit is the left-hand derivative at \[x=c\]?
What is the practical condition for differentiability at a point?
For differentiability on a closed interval \[[a,b]\], which derivative is considered at \[a\]?
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?
Which statement correctly describes the converse of “differentiability implies continuity”?
For \[f(x)=|x|\], what is the left-hand derivative at \[x=0\]?
For \[f(x)=|x|\], what is the right-hand derivative at \[x=0\]?
When does a derivative exist?
What does differentiability at a point mean?
