Advertisements
Advertisements
प्रश्न
Differentiate the following w.r.t. x:
sin (tan–1 e–x)
Advertisements
उत्तर
Let, y = sin (tan–1 e–x)
Differentiating both sides with respect to x,
`dy/dx = d/dx sin(tan^-1 e^(-x))`
= `cos (tan^-1 e^-x) d/dx tan^-1 e^-x`
= `cos (tan^-1 e^-x) 1/(1 + (e^-x)^2) d/dx (e^-x)`
= `cos (tan^-1 e^-x) 1/(1 + e^(-2x)) (e^-x) d/dx (-x)`
= `cos (tan^-1 e^-x) e^-x/(1 + e^(-2x)) (-1)`
= `-(e^-x cos (tan^-1 e^-x))/(1 + e^(-2x))`
APPEARS IN
संबंधित प्रश्न
Differentiate 3x w.r.t. log3x
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:
log (cos ex)
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:
(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 `"y" ="x"^"x" , "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 ______.
If x = `e^(x/y)`, then 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 `sqrt(("x + y")) + sqrt (("y - x")) = "a", "then" "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 \[\frac{d}{dx}(e^x)\]?
Which expression gives the quotient rule for logarithms?
What is the domain of the exponential function \[y=b^x\]?
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 range of the logarithmic function \[y=\log_b x\]?
The graph of \[y=\log_b x\] is a mirror image of which graph reflected perfectly across \[y=x\]?
Differentiate \[e^{-x}\] with respect to \[x\].
Differentiate \[\cos^{-1}(e^x)\] with respect to \[x\].
