Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
विकल्प
xx(1 – log x) + 10xlog10
xx(1 + log x) – 10xlog10
x(1 + log x) + 10xlog10
xx(1 + log x) + 10xlog10
Advertisements
उत्तर
xx(1 + log x) + 10xlog10
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
Find `"dy"/"dx"`if, y = (2x + 5)x
Find `"dy"/"dx"`if, y = `10^("x"^"x") + 10^("x"^10) + 10^(10^"x")`
If y = `e^(ax)`, then `x * dy/dx` = ______.
State whether the following is True or False:
If y = e2, then `"dy"/"dx" = 2"e"`
The derivative of ax is ax log a.
Find `"dy"/"dx"` if y = `sqrt(((3"x" - 4)^3)/(("x + 1")^4("x + 2")))`
Find `"dy"/"dx"` if y = `"x"^"x" + ("7x" - 1)^"x"`
If xy = 2x – y, then `("d"y)/("d"x)` = ______
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
Find `(dy)/(dx)`, if xy = yx
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 = (log x)x + (x)logx
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+y)`
Find `dy/dx` if, `y = x^(e^x)`
Find `dy/(dx)` if, `x = e^(3t), y = e^sqrtt`.
