Advertisements
Advertisements
Question
Differentiate the function with respect to x.
cos (sin x)
Advertisements
Solution
Let, y = cos (sin x)
Let, sin x = t
∴ y = cos t
`dy/dt` = −sin t, `dt/dx` = cos x
`∴ dy/dx = dy/dt * dt/dx`
= −sin t · cos x
= −sin (sin x) cos x
APPEARS IN
RELATED QUESTIONS
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Differentiate the function with respect to x:
`(5x)^(3cos 2x)`
Differentiate the function with respect to x:
`(cos^(-1) x/2)/sqrt(2x+7)`, −2 < x < 2
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
Does there exist a function which is continuos everywhere but not differentiable at exactly two points? Justify your answer?
If sin y = xsin(a + y) prove that `(dy)/(dx) = sin^2(a + y)/sin a`
Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
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, ______.
cos |x| is differentiable everywhere.
sinn (ax2 + bx + c)
(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`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.
A function is said to be continuous for x ∈ R, if ____________.
If `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` is
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` is equal to
If sin y = x sin (a + y), then value of dy/dx is
Let S = {t ∈ R : f(x) = |x – π| (e|x| – 1)sin |x| is not differentiable at t}. Then the set S is equal to ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
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.
If \[u\] and \[v\] are differentiable functions, which formula is correct?
What is \[\frac{d}{dx}(\tan x)\]?
When is a function differentiable on an open interval \[(a,b)\]?
If a function \[f\] is differentiable at a point \[c\], what must be true at that point?
For \[x\ne c\], which identity is used to prove that differentiability implies continuity?
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?
