Advertisements
Advertisements
प्रश्न
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
उत्तर
y = `"e"^(5"x"^2 - 2"x" + 4)`
Differentiating both sides w.r.t.x, we get
`"dy"/"dx" = "d"/"dx"("e"^(5"x"^2 - 2"x" + 4))`
`= "e"^(5"x"^2 - 2"x" + 4) * "d"/"dx"(5"x"^2 - 2"x" + 4)`
`= "e"^(5"x"^2 - 2"x" + 4) * [5(2"x") - 2 + 0]`
∴ `"dy"/"dx" = (10"x" - 2)* "e"^(5"x"^2 - 2"x" + 4)`
APPEARS IN
संबंधित प्रश्न
Find `dy/dx if x^2y^2 - tan^-1(sqrt(x^2 + y^2)) = cot^-1(sqrt(x^2 + y^2))`
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
If `"x"^"m"*"y"^"n" = ("x + y")^("m + n")`, then `"dy"/"dx" = "______"/"x"`
If x = cos−1(t), y = `sqrt(1 - "t"^2)` then `("d"y)/("d"x)` = ______
If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x such that the composite function y = f[g(x)] is a differentiable function of x, then `("d"y)/("d"x) = ("d"y)/("d"u)*("d"u)/("d"x)`. Hence find `("d"y)/("d"x)` if y = sin2x
Suppose y = f(x) is a differentiable function of x on an interval I and y is one – one, onto and `("d"y)/("d"x)` ≠ 0 on I. Also if f–1(y) is differentiable on f(I), then `("d"x)/("d"y) = 1/(("d"y)/("d"x)), ("d"y)/("d"x)` ≠ 0
If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______
If y = x2, then `("d"^2y)/("d"x^2)` is ______
y = sin (ax+ b)
If `y = root5(3x^2 + 8x + 5)^4`, find `dy/dx`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Solve the following:
If y = `root5((3x^2 +8x+5)^4`,find `dy/dx`
If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`.
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`
Find `dy/dx` if, `y = e^(5x^2 - 2x+4)`
