Advertisements
Advertisements
प्रश्न
DIfferentiate x sin x w.r.t. tan x.
Advertisements
उत्तर
Let u = x sin x and v = tan x.
Then we want to find `"du"/"dv"`
Differentiating u and v w.r.t. x, we get
`"du"/"dx" = "d"/"dx"(x sin x)`
= `x"d"/"dx"(sin x) + (sin x)."d"/"dx"(x)`
= x cos x + (sin x) x 1
= x cos x + sin x
and
`"dv"/"dx" = "d"/"dx"(tanx)` = sec2x
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")`
= `(x cos x + sin x)/(sec^2x)`.
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
Find `bb(dy/dx)` in the following:
sin2 y + cos xy = k
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Write the derivative of f (x) = |x|3 at x = 0.
Let \[f\left( x \right)\begin{cases}a x^2 + 1, & x > 1 \\ x + 1/2, & x \leq 1\end{cases}\] . Then, f (x) is derivable at x = 1, if
Find `"dy"/"dx"` ; if y = cos-1 `("2x" sqrt (1 - "x"^2))`
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
If ex + ey = ex+y, then show that `"dy"/"dx" = -e^(y - x)`.
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = sinθ, y = tanθ
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Differentiate xx w.r.t. xsix.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.
Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show" (d^2y)/(dx^2)` = 0.
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 0.
Find the nth derivative of the following : `(1)/(3x - 5)`
Find the nth derivative of the following : y = eax . cos (bx + c)
Differentiate the following w.r.t. x : `sin[2tan^-1(sqrt((1 - x)/(1 + x)))]`
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If `sqrt(y + x) + sqrt(y - x)` = c, show that `"dy"/"dx" = y/x - sqrt(y^2/x^2 - 1)`.
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`
Find `"dy"/"dx"` if, `"x"^"y" = "e"^("x - y")`
Find `"dy"/"dx"` if, xy = log (xy)
If log (x + y) = log (xy) + a then show that, `"dy"/"dx" = (- "y"^2)/"x"^2`.
Choose the correct alternative.
If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`
`(dy)/(dx)` of `2x + 3y = sin x` is:-
Find `(dy)/(dx)`, if `y = sin^-1 ((2x)/(1 + x^2))`
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then `(d^2y)/(dx^2)` at x = 0 is equal to ______.
If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.
Find `dy/dx` if, x = `e^(3t)`, y = `e^sqrtt`
If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`
Find `dy/dx` if, `x = e^(3t), y = e^(sqrtt)`
Find `dy/dx"if", x= e^(3t), y=e^sqrtt`
