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

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Solution

$\frac{d}{d x} [(a_{0} x^{n}) + \frac{d}{d x} (a_{1} x^{n - 1}) + \frac{d}{d x} (a_{2} x^{n - 2}) + . . . + a_{n - 1} x + a_{n}] = a_{0} \frac{d}{d x} (x^{n}) + a_{1} \frac{d}{d x} (x^{n - 1}) + a_{2} \frac{d}{d x} (x^{n - 2}) + . . . + a_{n - 1} \frac{d}{d x} (x) + \frac{d}{d x} (a_{n}) = n a_{0} x^{n - 1} + (n - 1) a_{1} x^{n - 2} + (n - 2) a_{2} x^{n - 3} + . . . . + a_{n - 1} (1) + 0 = n a_{0} x^{n - 1} + (n - 1) a_{1} x^{n - 2} + (n - 2) a_{2} x^{n - 3} + . . . . + a_{n - 1}$

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Similar questions

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a0 xn + a1 xn−1 + a2 xn−2 + ... + an−1 x + an.

ddxa0 xn+ddxa1 xn-1+ddxa2 xn-2+...+an-1 x+ an=a0ddxxn+a1ddxxn-1+a2ddxxn-2+...+an-1ddxx+ddxan=na0 xn-1+n-1 a1 xn-2+n-2a2 xn-3+....+an-11+0=na0 xn-1+n-1 a1 xn-2+n-2a2 xn-3+....+an-1

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