Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
पर्याय
xx(1 – log x) + 10xlog10
xx(1 + log x) – 10xlog10
x(1 + log x) + 10xlog10
xx(1 + log x) + 10xlog10
उत्तर
xx(1 + log x) + 10xlog10
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
If y = elogx then `dy/dx` = ?
Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`
Differentiate log (1 + x2) with respect to ax.
If y = `"a"^((1 + log"x"))`, then `("d"y)/("d"x)` is ______
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
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `("d"y)/("d"x)`, if y = [log(log(logx))]2
Find `("d"y)/("d"x)`, if xy = log(xy)
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx
Find `("d"y)/("d"x)`, if y = xx + (7x – 1)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)
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx` if, `y = x^(e^x)`
Find `dy/(dx)` if, `y = x^(e^x)`
