Advertisements
Advertisements
प्रश्न
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Advertisements
उत्तर
Let, y = `sec(tan (sqrtx))`
Differentiating both sides with respect to x,
`dy/dx = d/dx sec [tan (sqrtx)]`
= `sec (tan sqrtx) tan (tan sqrtx) d/dx tan sqrtx`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx d/dx (sqrtx)`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx * 1/2 x^(1/2-1)`
= `sec (tan sqrtx) tan (tan sqrtx) sec^2 sqrtx * 1/(2sqrtx)`
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
sin (ax + b)
Differentiate the function with respect to x.
cos x3 . sin2 (x5)
Differentiate the function with respect to x.
`2sqrt(cot(x^2))`
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:
(3x2 – 9x + 5)9
Differentiate the function with respect to x:
sin3 x + cos6 x
Differentiate the function with respect to x:
`x^(x^2 -3) + (x -3)^(x^2)`, for x > 3
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
If (x – a)2 + (y – b)2 = c2, for some c > 0, prove that `[1+ (dy/dx)^2]^(3/2)/((d^2y)/dx^2)` is a constant independent of a and b.
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)|`.
`"If y" = (sec^-1 "x")^2 , "x" > 0 "show that" "x"^2 ("x"^2 - 1) (d^2"y")/(d"x"^2) + (2"x"^3 - "x") (d"y")/(d"x") - 2 = 0`
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`
Differentiate `tan^-1 (sqrt(1 - x^2)/x)` with respect to`cos^-1(2xsqrt(1 - x^2))`, where `x ∈ (1/sqrt(2), 1)`
cos |x| is differentiable everywhere.
`cos(tan sqrt(x + 1))`
sinx2 + sin2x + sin2(x2)
`sin^-1 1/sqrt(x + 1)`
`tan^-1 (sqrt((1 - cosx)/(1 + cosx))), - pi/4 < x < pi/4`
`tan^-1 (secx + tanx), - pi/2 < x < pi/2`
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
For the curve `sqrt(x) + sqrt(y)` = 1, `"dy"/"dx"` at `(1/4, 1/4)` is ______.
If `ysqrt(1 - x^2) + xsqrt(1 - y^2)` = 1, then prove that `(dy)/(dx) = - sqrt((1 - y^2)/(1 - x^2))`
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 ______.
The function f(x) = x | x |, x ∈ R is differentiable ______.
If \[u\] and \[v\] are differentiable functions, what is \[(uv)'\]?
For \[v\ne0\], what is the derivative of \[\frac{u}{v}\]?
What is \[\frac{d}{dx}(\cos x)\]?
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?
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 \[x=0\]?
What does differentiability at a point mean?
