Advertisements
Advertisements
प्रश्न
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`
Find `"dy"/"dx"`if, y = `root(3)(("3x" - 1)/(("2x + 3")(5 - "x")^2))`
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
Fill in the Blank
If 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/square`
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
If y = `e^(ax)`, then `x * dy/dx` = ______.
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Differentiate log (1 + x2) with respect to ax.
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
If u = 5x and v = log x, then `("du")/("dv")` is ______
If u = ex and v = loge x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = log(log x), then `("d"y)/("d"x)` = logx
Find `("d"y)/("d"x)`, if xy = log(xy)
Find `("d"y)/("d"x)`, if x = `sqrt(1 + "u"^2)`, y = log(1 +u2)
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = xx + (7x – 1)x
If xa .yb = `(x + y)^((a + b))`, then show that `("d"y)/("d"x) = y/x`
Find `("d"y)/("d"x)`, if y = x(x) + 20(x)
Solution: Let y = x(x) + 20(x)
Let u = `x^square` and v = `square^x`
∴ y = u + v
Diff. w.r.to x, we get
`("d"y)/("d"x) = square/("d"x) + "dv"/square` .....(i)
Now, u = xx
Taking log on both sides, we get
log u = x × log x
Diff. w.r.to x,
`1/"u"*"du"/("d"x) = x xx 1/square + log x xx square`
∴ `"du"/("d"x)` = u(1 + log x)
∴ `"du"/("d"x) = x^x (1 + square)` .....(ii)
Now, v = 20x
Diff.w.r.to x, we get
`"dv"/("d"x") = 20^square*log(20)` .....(iii)
Substituting equations (ii) and (iii) in equation (i), we get
`("d"y)/("d"x)` = xx(1 + log x) + 20x.log(20)
Solve the following differential equations:
x2ydx – (x3 – y3)dy = 0
`int 1/(4x^2 - 1) dx` = ______.
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx if, y = x^(e^x)`
Find `dy / dx` if, `y = x^(e^x)`
Find `dy/dx "if", y = x^(e^x)`
