Question

Find the nth derivative of 4x3– 3x2 +2x -8 with respect to x.​

Answer 1

Solution

Find :-

• Derivative of 4x³ - 3x² + 2x - 8 upto nth terms with respect to x .

Explanation

Using Formula

★ If, y = x^n, then derivative be, dy/dx = n.x^(n-1)

Now, let

==> y = 4x³ - 3x² + 2x - 8

Now, differentiate both sids with respect to x .

==> dy/dx = d/dx(4x³ - 3x² + 2x - 8)

take seperate differentiation .

==> dy/dx = d/dx(4x³) - d/dx(3x²) + d/dx(2x) - d/dx(8)

we Know,

Differentiation of any constant it will be always zeros

Or,

★ d a/dx = 0 , where, a be constant Number .

So, Now

==> dy/dx = 4.3.x² - 3.2.x + 2 - 0

==> dy/dx = 12x² - 6x + 2

Now, again defferentiate w.r. to x .

==> d²y/dx² = d/dx(12x²) - d/dx(6x) + d/dx (2)

==> d²y/dx² = 12.2.x - 6 + 0

==> d²y/dx² = 24x - 6

Again,

==> d³y/dx³ = d/dx(24x) - d/dx(6)

==> d³y/dx³ = 24 - 0

==> d³y/dx³ = 24

Again,

==> d⁴y/dx⁴ = d/dx(24)

==> d⁴y/dx⁴ = 0

If, we calculate upto nth time differentiation it will be zeroes.

So, we can write this differentiation ,

==> d^n/dx^n (y) = 0

Or,

==> y^n = 0

Hence

• nth derivation of 4x³ - 3x² + 2x - 8 will be 0.

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