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:
sin (tan–1 e–x)
Differentiate the following w.r.t. x:
`e^x + e^(x^2) + "..." + e^(x^5)`
Differentiate the following w.r.t. x:
log (log x), x > 1
If `"y" ="x"^"x" , "find" "dy"/"dx"`.
If xy - yx = ab, find `(dy)/(dx)`.
The derivative of log10x w.r.t. x is ______.
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" = (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 `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find" "dy"/"dx"`
If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.
What is \[\frac{d}{dx}(e^x)\]?
What is \[\frac{d}{dx}(\log x)\] for \[x>0\]?
Which expression gives the change of base rule?
Which expression gives the quotient rule for logarithms?
Which expression gives the power rule for logarithms?
Which inverse property is valid only for \[x>0\]?
What is the range of the exponential function \[y=b^x\]?
Through which point does every graph of \[y=b^x\] pass?
What is the domain of the logarithmic function \[y=\log_b x\]?
What is the range of the logarithmic function \[y=\log_b x\]?
Through which point does every graph of \[y=\log_b x\] pass?
The graph of \[y=\log_b x\] is a mirror image of which graph reflected perfectly across \[y=x\]?
If \[y=b^x\], which equivalent logarithmic statement is correct?
Differentiate \[e^{-x}\] with respect to \[x\].
For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].
Which list contains the main log laws?
