Advertisements
Advertisements
प्रश्न
Find `(d^2y)/(dx^2)` , if y = log x
उत्तर
∵ y = log x
∵ `(dy)/(dx) = 1/x = x^-1`
and `(d^2y)/(dx^2) = -x^-2 = (-1)/x^2`
APPEARS IN
संबंधित प्रश्न
If `y=log[x+sqrt(x^2+a^2)] ` show that `(x^2+a^2)(d^2y)/(dx^2)+xdy/dx=0`
Differentiate the function with respect to x.
`x^x - 2^(sin x)`
Differentiate the function with respect to x.
`(x + 1/x)^x + x^((1+1/x))`
Differentiate the function with respect to x.
`(x cos x)^x + (x sin x)^(1/x)`
Differentiate (x2 – 5x + 8) (x3 + 7x + 9) in three ways mentioned below:
- by using product rule
- by expanding the product to obtain a single polynomial.
- by logarithmic differentiation.
Do they all give the same answer?
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Find `dy/dx` if y = xx + 5x
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Find `"dy"/"dx"` , if `"y" = "x"^("e"^"x")`
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
If `log_10((x^3 - y^3)/(x^3 + y^3)) = 2, "show that" "dy"/"dx" = -(99x^2)/(101y^2)`
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If x = `asqrt(secθ - tanθ), y = asqrt(secθ + tanθ), "then show that" "dy"/"dx" = -y/x`.
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
`lim_("x" -> 0)(1 - "cos x")/"x"^2` is equal to ____________.
If `"y" = "e"^(1/2log (1 + "tan"^2"x")), "then" "dy"/"dx"` is equal to ____________.
Given f(x) = `log((1 + x)/(1 - x))` and g(x) = `(3x + x^3)/(1 + 3x^2)`, then fog(x) equals
If y = `(1 + 1/x)^x` then `(2sqrt(y_2(2) + 1/8))/((log 3/2 - 1/3))` is equal to ______.
Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.
Find the derivative of `y = log x + 1/x` with respect to x.