Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x:
`cos x/log x`, x > 0
Advertisements
उत्तर
Let, y = `cos x/log x`
Differentiating both sides with respect to x,
`dy/dx = d/dx cos x/log x`
= `(log x d/dx cos x - cos x d/dx log x)/(log x)^2`
= `(log x (- sin x) - cos x xx 1/x)/((log x)^2)`
= `(- sin x log x - cos x/x)/(log x)^2`
= `(- (x sin x log x + cos x))/(x (log x)^2)`, x > 0
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^(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 ex)
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:
cos (log x + ex), x > 0
Differentiate the function with respect to x:
(log x)log x, x > 1
Differentiate the function with respect to x:
cos (a cos x + b sin x), for some constant a and b.
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 xy - yx = ab, find `(dy)/(dx)`.
If xy = ex–y, prove that `("d"y)/("d"x) = logx/(1 + logx)^2`
The derivative of log10x w.r.t. x is ______.
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 `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.
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 ____________.
