Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x:
`e^(sin^(-1) x)`
Advertisements
उत्तर
Let, y = `e^(sin^(-1) x)`
Differentiating both sides with respect to x,
`dy/dx = d/dx e^(sin^(-1) x)`
= `e^(sin^-1 x) d/dx sin^-1 x`
= `e^(sin^-1)x* 1/sqrt(1 - x^2)`
APPEARS IN
संबंधित प्रश्न
Differentiate 3x w.r.t. log3x
Differentiate the following w.r.t. x:
`e^x/sinx`
Differentiate the following w.r.t. x:
`e^(x^3)`
Differentiate the following w.r.t. x:
`e^x + e^(x^2) + "..." + e^(x^5)`
Differentiate the following w.r.t. x:
`sqrt(e^(sqrtx))`, x > 0
Differentiate the following w.r.t. x:
log (log x), x > 1
Differentiate the following w.r.t. x:
`cos x/log x`, x > 0
Differentiate the following w.r.t. x:
cos (log x + ex), x > 0
Differentiate the function with respect to x:
cos (a cos x + b sin x), for some constant a and b.
If `"y" ="x"^"x" , "find" "dy"/"dx"`.
If xy - yx = ab, find `(dy)/(dx)`.
If `"x" = "e"^(cos2"t") "and" "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.
If xy = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
If yx = ey – x, prove that `"dy"/"dx" = (1 + log y)^2/logy`
If y = `(cos x)^((cos x)^((cosx)....oo)`, show that `"dy"/"dx" = (y^2 tanx)/(y log cos x - 1)`
Find `"dy"/"dx"`, if y = `x^tanx + sqrt((x^2 + 1)/2)`
If `"y" = ("x" + sqrt(1 + "x"^2))^"n", "then" (1 + "x"^2) ("d"^2 "y")/"dx"^2 + "x" ("dy")/("dx")` is ____________.
If `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.
If `"x" = "a" ("cos" theta + theta "sin" theta), "y = a" ("sin" theta - theta "cos" theta), "then" ("d"^2 "y")/("dx"^2) =` ____________.
If `"y"^2 = "ax"^2 + "bx + c", "then" "d"/"dx" ("y"^3 "y"_"z") =` ____________.
If `sqrt(("x + y")) + sqrt (("y - x")) = "a", "then" "dy"/"dx" =` ____________.
If `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find" "dy"/"dx"`
If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.
The domain of the function defined by f(x) = logx 10 is
Which function is an exponential function?
For positive values of \[x\], which expression grows faster than \[x^n\] for any fixed positive integer \[n\] when \[x\] is sufficiently large?
What is \[\frac{d}{dx}(\log x)\] for \[x>0\]?
Which expression gives the quotient rule for logarithms?
Which expression gives the power rule for logarithms?
Which inverse property is valid only for \[x>0\]?
Through which point does every graph of \[y=b^x\] pass?
For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].
Differentiate \[e^{\cos x}\] with respect to \[x\].
