Advertisements
Advertisements
प्रश्न
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
पर्याय
True
False
उत्तर
False
APPEARS IN
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `(1 + 1/"x")^"x"`
If y = elogx then `dy/dx` = ?
If y = log `("e"^"x"/"x"^2)`, then `"dy"/"dx" = ?`
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
Differentiate log (1 + x2) with respect to ax.
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 = 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)
`int 1/(4x^2 - 1) dx` = ______.
If y = x . log x then `dy/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)`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/(dx) "if", y = x^(e^(x))`
