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प्रश्न
State whether the following is True or False:
If y = e2, then `"dy"/"dx" = 2"e"`
पर्याय
True
False
उत्तर
False
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
Fill in the Blank
If 0 = log(xy) + a, then `"dy"/"dx" = (-"y")/square`
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
Solve the following:
If y = [log(log(logx))]2, find `"dy"/"dx"`
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 ______
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 = 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)
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If y = (log x)2 the `dy/dx` = ______.
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Find `dy/(dx) "if", y = x^(e^(x))`
