Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x:
`e^x/sinx`
उत्तर
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
संबंधित प्रश्न
Differentiate the following w.r.t. x:
`e^(sin^(-1) x)`
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:
`log(cos e^x)`
Differentiate the following w.r.t. x:
`e^x + e^(x^2) +... + e^(x^3)`
Differentiate the following w.r.t. x:
log (log x), x > 1
Differentiate w.r.t. x the function:
(log x)log x, x > 1
Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.
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`
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)`
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 = a"^"x", "b"^(2"x" -1), "then" ("d"^2"y")/"dx"^2` is ____________.
If `"x" = "a" ("cos" theta + theta "sin" theta), "y = a" ("sin" theta - theta "cos" theta), "then" ("d"^2 "y")/("dx"^2) =` ____________.
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