Advertisements
Advertisements
प्रश्न
Differentiate 3x w.r.t. logx3.
Advertisements
उत्तर
Let u = 3x and v = logx3.
Then we want to find `"du"/"dv"`.
Differentiating u and v w.r.t. x, we get
`"du"/"dv" = "d"/"dx"(3^x)`
= 3x.log3
and
`"dv"/"dx" = "d"/"dx"(log_x3)`
= `"d"/"dx"((log3)/(logx))`
= `log3."d"/"dx"(logx)^-1`
= `(log3)(-1)(logx)^-2."d"/"dx"(logx)`
= `(-log3)/(logx)^2 xx (1)/x`
= `(-log3)/(x(logx)^2`
∴ `"du"/"dv" = (("du"/"dx"))/(("dv"/"dx")`
= `(3^x.log3)/([(-log3)/(x(logx)^2)]`
= – x(log x)2.3x.
APPEARS IN
संबंधित प्रश्न
Differentiate the following function with respect to x: `(log x)^x+x^(logx)`
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
`sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5)))`
Differentiate the function with respect to x.
xx − 2sin x
Differentiate the function with respect to x.
`x^(xcosx) + (x^2 + 1)/(x^2 -1)`
Find `bb(dy/dx)` for the given function:
xy + yx = 1
Find `bb(dy/dx)` for the given function:
(cos x)y = (cos y)x
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Evaluate
`int 1/(16 - 9x^2) dx`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Differentiate : log (1 + x2) w.r.t. cot-1 x.
If `"x"^(5/3) . "y"^(2/3) = ("x + y")^(7/3)` , the show that `"dy"/"dx" = "y"/"x"`
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If y = (log x)x + xlog x, find `"dy"/"dx".`
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
`"If" y = sqrt(logx + sqrt(log x + sqrt(log x + ... ∞))), "then show that" dy/dx = (1)/(x(2y - 1).`
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = esin3t, y = ecos3t, then show that `dy/dx = -(ylogx)/(xlogy)`.
If x = 2cos4(t + 3), y = 3sin4(t + 3), show that `"dy"/"dx" = -sqrt((3y)/(2x)`.
If x = sin–1(et), y = `sqrt(1 - e^(2t)), "show that" sin x + dy/dx` = 0
Find the second order derivatives of the following : x3.logx
Find the second order derivatives of the following : log(logx)
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
If y = A cos (log x) + B sin (log x), show that x2y2 + xy1 + y = 0.
If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.
If y = log [cos(x5)] then find `("d"y)/("d"x)`
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`2^(cos^(2_x)`
`log (x + sqrt(x^2 + "a"))`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.
If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.
The derivative of x2x w.r.t. x is ______.
Find `dy/dx`, if y = (log x)x.
Find the derivative of `y = log x + 1/x` with respect to x.
If \[y=x^x+x^{\frac{1}{x}}\] then \[\frac{\mathrm{d}y}{\mathrm{d}x}\] is equal to
Which is the derivative of \[\sqrt{\frac{(x-3)(x^2+4)}{3x^2+4x+5}}\]?
For \[y=x^{\sin x}\], \[x>0\], what equation results after taking logarithm on both sides?
After taking logarithms in logarithmic differentiation, which rules are used to simplify products, quotients and powers before differentiation?
What condition must be ensured for an expression inside logarithm?
