Advertisements
Advertisements
Question
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Solution
y = log(ax2 + bx + c)
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"` [log(ax2 + bx + c)]
`= 1/("ax"^2 + "bx" + "c") * "d"/"dx" ("ax"^2 + "bx" + "c")`
`= 1/("ax"^2 + "bx" + "c") * ["a"("2x") + "b" + 0]`
∴ `"dy"/"dx" = ("2ax" + "b")/("ax"^2 + "bx" + "c")`
APPEARS IN
RELATED QUESTIONS
Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
Find `"dy"/"dx"` if cos (xy) = x + y
Choose the correct alternative.
If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =
Find `"dy"/"dx"`, if y = `2^("x"^"x")`.
If y = sec (tan−1x) then `("d"y)/("d"x)` at x = 1 is ______.
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
Choose the correct alternative:
If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?
If y = x10, then `("d"y)/("d"x)` is ______
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
If y = `sec^-1 ((sqrt(x) + 1)/(sqrt(x + 1))) + sin^-1((sqrt(x) - 1)/(sqrt(x) + 1))`, then `"dy"/"dx"` is equal to ______.
Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.
If y = 2x2 + a2 + 22 then `dy/dx` = ______.
Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `dy/dx` if, y = `e^(5x^2-2x+4)`
Solve the following:
If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`
If `y = root{5}{(3x^2 + 8x + 5)^4}, "find" dy/dx`.
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
