Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
उत्तर
Let, y = `2 sqrt(cot (x^2))`
y = 2 (cot x2)1/2
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/(cossqrtx^2/sinsqrtx^2)`
= `(-2x)/((sinx^2)sqrt(sinx^2) sqrt(cosx^2)`
= `(-2xsqrt2)/(sinx^2 sqrt(2sinx^2 cosx^2))`
= `(-2sqrt(2x))/(sinx^2 sqrt(sin2x^2))`
APPEARS IN
संबंधित प्रश्न
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.
`sec(tan (sqrtx))`
Differentiate the function with respect to x.
`cos (sqrtx)`
Differentiate w.r.t. x the function:
(3x2 – 9x + 5)9
Differentiate w.r.t. x the function:
`(5x)^(3cos 2x)`
Differentiate w.r.t. x the function:
`(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 y = `[(f(x), g(x), h(x)),(l, m,n),(a,b,c)]`, prove that `dy/dx` =`|(f'(x), g'(x), h'(x)),(l,m, n),(a,b,c)|`
Discuss the continuity and differentiability of the
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)`
Differential coefficient of sec (tan–1x) w.r.t. x is ______.
|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.
`sin^-1 1/sqrt(x + 1)`
sinmx . cosnx
(x + 1)2(x + 2)3(x + 3)4
`cos^-1 ((sinx + cosx)/sqrt(2)), (-pi)/4 < x < pi/4`
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`sec^-1 (1/(4x^3 - 3x)), 0 < x < 1/sqrt(2)`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
If y = `sqrt(sinx + y)`, then `"dy"/"dx"` is equal to ______.
If k be an integer, then `lim_("x" -> "k") ("x" - ["x"])` ____________.
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 ____________.
The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in 5 hours then in 25 hours, its number would be
If sin y = x sin (a + y), then value of dy/dx is
If f(x) = `{{:((sin(p + 1)x + sinx)/x,",", x < 0),(q,",", x = 0),((sqrt(x + x^2) - sqrt(x))/(x^(3//2)),",", x > 0):}`
is continuous at x = 0, then the ordered pair (p, q) is equal to ______.
The function f(x) = x | x |, x ∈ R is differentiable ______.
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 ______.
