Advertisements
Advertisements
प्रश्न
Find `("d"y)/("d"x)`, if y = (6x3 – 3x2 – 9x)10
Advertisements
उत्तर
y = (6x3 – 3x2 – 9x)10
Differentiating both sides w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)[(6x^3 - 3x^2 - 9x)^10]`
= `10(6x^3 - 3x^2 - 9x)^9 xx "d"/("d"x) (6x^3 - 3x^2 - 9x)`
= 10(6x3 − 3x2 − 9x)9 × [6(3x2) – 3(2x) − 9]
∴ `("d"y)/("d"x)` = = 10(6x3 − 3x2 − 9x)9 . (18x2 − 6x − 9)
APPEARS IN
संबंधित प्रश्न
Find `dy/dx`, if `xsqrt(x) + ysqrt(y) = asqrt(a)`.
Find `"dy"/"dx"`If x3 + x2y + xy2 + y3 = 81
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 xey + yex = 1
Find `"dy"/"dx"` if cos (xy) = x + y
Find `"dy"/"dx"` if `e^(e^(x - y)) = x/y`
Find the second order derivatives of the following : xx
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
Choose the correct alternative.
If y = `sqrt("x" + 1/"x")`, then `"dy"/"dx" = ?`
Find `"dy"/"dx"`, if y = xx.
If y = cos−1 [sin (4x)], find `("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 = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
If y = x10, then `("d"y)/("d"x)` is ______
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
If x = a sec3θ and y = a tan3θ, find `("d"y)/("d"x)` at θ = `pi/3`
y = `sec (tan sqrt(x))`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
Solve the following:
If`y=root(5)((3x^2+8x+5)^4),"find" (dy)/dx`
Find `"dy"/"dx"` if, `"y" = "e"^(5"x"^2 - 2"x" + 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 = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
Find `"dy"/"dx"` if, y = `"e"^(5"x"^2 - 2"x" + 4)`
Solve the following.
If `y=root(5)((3x^2 + 8x + 5)^4)`, find `dy/dx`
Solve the following:
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/(dx)`.
