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प्रश्न
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
पर्याय
True
False
उत्तर
True
APPEARS IN
संबंधित प्रश्न
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Find `"dy"/"dx"`if, y = `"e"^("x"^"x")`
Find `"dy"/"dx"`if, y = `root(3)(("3x" - 1)/(("2x + 3")(5 - "x")^2))`
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If y = x log x, then `(d^2y)/dx^2`= _____.
State whether the following is True or False:
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If u = 5x and v = log x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `(dy)/(dx)`, if xy = yx
Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx
Find `("d"y)/("d"x)`, if y = `x^(x^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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