Differentiate the following functions with respect to x :

$a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . . + a_{n - 1} x + a_{n} .$

Open in App

Solution

We have,

$\frac{d}{d x} (a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . . + a_{n - 1} x + a_{n})$

$= a_{0} \frac{d (x)^{n}}{d x} + a_{1} \frac{d (x)^{n - 1}}{d x} = a_{2} \frac{d (x)^{n - 2}}{d x} + . . . . + a_{n - 1} \frac{d (x)}{d x} + a n \frac{d (1)}{d x}$

$= n a_{0} x^{n - 1} + (n - 1) a_{1} x^{n - 2} + . . . . + a_{n - 1} + 0$

$= n a_{0} x^{n - 2} + (n - 1) a_{1} x^{n - 2} + . . . . . + a_{n - 1}$

Suggest Corrections

Similar questions

Q. a₀ xⁿ + a₁ xⁿ⁻¹ + a₂ xⁿ⁻² + ... + a_n₋₁ x + a_n.

Q. Find the derivative of

| x | + a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . . + a_{n - 1} x + a_{n}

Q. If

x + 1

is a factor of

f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + \dots + a_{n} = 0

, then

The highest index of the variable x occurring in the polynomial $f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . . . . . . a_{n - 1} x + a_{n}$ is called ___________.

Q. Write the necessary and sufficient condition for the polynomial

p (x) = a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . + a_{n}

to be a polynomial of order

(n - 2)

Join BYJU'S Learning Program

Differentiate the following functions with respect to x : a0xn+a1xn−1+a2xn−2+....+an−1x+an.

We have, ddx(a0xn+a1xn−1+a2xn−2+....+an−1x+an) =a0d(x)ndx+a1d(x)n−1dx=a2d(x)n−2dx+....+an−1d(x)dx+and(1)dx =na0xn−1+(n−1)a1xn−2+....+an−1+0 =na0xn−2+(n−1)a1xn−2+.....+an−1

Differentiate the following functions with respect to x :

$a_{0} x^{n} + a_{1} x^{n - 1} + a_{2} x^{n - 2} + . . . . + a_{n - 1} x + a_{n} .$