Advertisements
Advertisements
प्रश्न
Find `("d"^2y)/("d"x^2)`, if y = `"e"^((2x + 1))`
Advertisements
उत्तर
y = `"e"^((2x + 1))`
Differentiating both sides w.r.t. x, we get
`("d"y)/("d"x) = "e"^((2x + 1))*"d"/("d"x)(2x + 1)`
∴ `("d"y)/("d"x) = "e"^((2x + 1))*(2 + 0)`
∴ `("d"y)/("d"x) = 2"e"^((2x + 1))`
Again, differentiating both sides w.r.t. x , we get
∴ `("d"^2y)/("d"x^2) = 2*"d"/("d"x)"e"^((2x + 1))`
= `2"e"^((2x + 1))*"d"/("d"x)(2x + 1)`
= `2"e"^((2x + 1))*(2 + 0)`
∴ `("d"^2y)/("d"x^2) = 4"e"^((2x + 1))`
संबंधित प्रश्न
if `y = tan^2(log x^3)`, find `(dy)/(dx)`
Find `dy/dx`, if `xsqrt(x) + ysqrt(y) = asqrt(a)`.
Find `dy/dx if x + sqrt(xy) + y = 1`
Find `"dy"/"dx"` if ex+y = cos(x – y)
Find the second order derivatives of the following : e4x. cos 5x
Find `"dy"/"dx"` if, y = log(ax2 + bx + c)
Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`
`d/dx(10^x) = x*10^(x - 1)`
Find `"dy"/"dx"`, if y = xx.
Differentiate `"e"^("4x" + 5)` with respect to 104x.
If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______
State whether the following statement is True or False:
If y = ex, then `("d"^2y)/("d"x^2)` = ex
If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.
`"d"/("d"x) [sin(1 - x^2)]^2` = ______.
Differentiate `sqrt(tansqrt(x))` w.r.t. x
Find `("d"y)/("d"x)`, if y = `tan^-1 ((3x - x^3)/(1 - 3x^2)), -1/sqrt(3) < x < 1/sqrt(3)`
If f(x) = |cos x – sinx|, find `"f'"(pi/6)`
If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.
If f(x) = `{{:(x^3 + 1",", x < 0),(x^2 + 1",", x ≥ 0):}`, g(x) = `{{:((x - 1)^(1//3)",", x < 1),((x - 1)^(1//2)",", x ≥ 1):}`, then (gof) (x) is equal to ______.
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`
lf 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 prove that:
`dy/dx = dy/(du) xx (du)/dx`
Hence, find `d/dx[log(x^5 + 4)]`.
If y = `root5((3x^2 + 8x +5)^4)`, find `dy/dx`.
If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`
Find `dy/dx` if, `y = e^(5x^2 - 2x +4)`
Find `dy/dx` if, `y=e^(5x^2-2x+4)`
If `y = (x + sqrt(a^2 + x^2))^m`, prove that `(a^2 + x^2)(d^2y)/(dx^2) + xdy/dx - m^2y = 0`
Find `dy/dx` if, `y = e^(5x^2 - 2x + 4)`.
