Advertisements
Advertisements
Question
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
Advertisements
Solution
Let, y = `2 sqrt(cot (x^2))`
On differentiating with respect to x,
`dy/dx = 2 d/dx sqrt (cot(x)^2)`
= `2* 1/2 {cot (x^2)}^(-1/2)* d/dx cot (x^2)`
= `1/(sqrtcot(x^2))* {-"cosec"^2(x^2)} d/dx (x^2)`
= `1/sqrt(cot(x^2))* {- "cosec"^2 (x^2)} (2x)`
= `(-2x "cosec"^2 (x)^2)/(sqrtcot(x^2))`
= `(-2x)/(sin^2 x^2) xx 1/(sqrt(cosx^2)/sqrt(sinx^2))`
= `(-2x)/((sinx^2)sqrt(sinx^2) sqrt(cosx^2)`
= `(-2xsqrt2)/(sinx^2 sqrt(2 sinx^2 cosx^2))`
= `(-2sqrt(2x))/(sinx^2 sqrt(sin2x^2))`
APPEARS IN
RELATED QUESTIONS
Differentiate the function with respect to x.
sin (x2 + 5)
Differentiate the function with respect to x.
cos (sin x)
Differentiate the function with respect to x.
`(sin (ax + b))/cos (cx + d)`
Prove that the function f given by f(x) = |x − 1|, x ∈ R is not differentiable at x = 1.
Differentiate the function with respect to x:
`sin^(–1)(xsqrtx), 0 ≤ x ≤ 1`
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`.
If y = tanx + secx, prove that `("d"^2y)/("d"x^2) = cosx/(1 - sinx)^2`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
Let f(x)= |cosx|. Then, ______.
If u = `sin^-1 ((2x)/(1 + x^2))` and v = `tan^-1 ((2x)/(1 - x^2))`, then `"du"/"dv"` is ______.
cos |x| is differentiable everywhere.
(sin x)cosx
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`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 ______.
If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
`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 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 ______.
A particle is moving on a line, where its position S in meters is a function of time t in seconds given by S = t3 + at2 + bt + c where a, b, c are constant. It is known that at t = 1 seconds, the position of the particle is given by S = 7 m. Velocity is 7 m/s and acceleration is 12 m/s2. The values of a, b, c are ______.
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) = `{{:(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.
If f(x) = `{{:(x^2"," if x ≥ 1),(x"," if x < 1):}`, then show that f is not differentiable at x = 1.
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 ______.
Differentiability determines whether a function has what at a particular point?
If \[u\] and \[v\] are differentiable functions, which formula is correct?
If \[u\] and \[v\] are differentiable functions, what is \[(uv)'\]?
A function is differentiable at \[x=c\] when which condition holds?
Which limit is the right-hand derivative at \[x=c\]?
For \[x\ne c\], which identity is used to prove that differentiability implies continuity?
Which conclusion establishes that \[f\] is continuous at \[x=c\]?
When does a derivative exist?
