Advertisements
Advertisements
Question
Differentiate the following w.r.t. x:
`e^x/sinx`
Solution
Let,`e^x/sin x`
Differentiating both sides with respect to x,
`dy/dx = (sin x d/dx e^x - e^x d/dx sin x)/(sin^2 x)`
`= (sin x e^x - e^x . cos x)/(sin^2 x)`
`= (e^x (sin x - cos x))/(sin^2x), xne xpi, n inZ.`
APPEARS IN
RELATED QUESTIONS
Differentiate 3x w.r.t. log3x
Differentiate the following w.r.t. x:
`e^(x^3)`
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
`e^x + e^(x^2) +... + e^(x^3)`
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
If xy - yx = ab, find `(dy)/(dx)`.
The derivative of log10x w.r.t. x is ______.
If x = `"e"^(x/y)`, prove that `"dy"/"dx" = (x - y)/(xlogx)`
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)`
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 `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find" "dy"/"dx"`
If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then" "dy"/"dx"` is equal to ____________.
If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.
The domain of the function defined by f(x) = logx 10 is
