Advertisements
Advertisements
Question
Differentiate the function with respect to x.
`sec(tan (sqrtx))`
Solution
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 x^(1//2)`
`= dy/dx = sec [tan (sqrtx)] tan [tan sqrtx] sec^2 sqrtx * 1/(2sqrtx)`
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)`
Differentiate the function with respect to x.
`cos x^3. sin^2 (x^5)`
Prove that the function f given by `f(x) = |x - 1|, x in R` is not differentiable at x = 1.
Differentiate w.r.t. x the function:
(3x2 – 9x + 5)9
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?
Discuss the continuity and differentiability of the
If f(x) = x + 1, find `d/dx (fof) (x)`
Let f(x) = x|x|, for all x ∈ R. Discuss the derivability of f(x) at x = 0
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.
`cos(tan sqrt(x + 1))`
sinx2 + sin2x + sin2(x2)
`sin^-1 1/sqrt(x + 1)`
(sin x)cosx
`cos^-1 ((sinx + cosx)/sqrt(2)), (-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 ((3"a"^2x - x^3)/("a"^3 - 3"a"x^2)), (-1)/sqrt(3) < x/"a" < 1/sqrt(3)`
`tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2))), -1 < x < 1, x ≠ 0`
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 `y = (x + sqrt(1 + x^2))^n`, then `(1 + x^2) (d^2y)/(dx^2) + x (dy)/(dx)` 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
`d/(dx)[sin^-1(xsqrt(1 - x) - sqrt(x)sqrt(1 - x^2))]` 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 ______.
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.
The function f(x) = x | x |, x ∈ R is differentiable ______.
If f(x) = | cos x |, then `f((3π)/4)` is ______.
Prove that the greatest integer function defined by f(x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
