Question

Find the nth derivative of e^x(2x+3)^3

Answer 1

$(8x^{3} +84x^{2} +246x+207)e^{x}$.

• The nth derivative of a function can be any of its higher order derivatives.
• The first derivative is obtained by taking the function's derivative once. You can obtain the second derivative by differentiating the new function once again. The third derivative, fourth derivative, or fifth derivative are obtained by applying the differentiation rules a third, fourth, or fifth time, respectively. The formula for each additional derivative of a function is known as the nth derivative.
• Finding the nth derivative entails looking for a pattern among a few derivatives (first, second, third, etc.). You have a formula for the nth derivative if one is present. Find the first few derivatives to spot the pattern, then find the nth derivative. Apply the standard differentiation principles to a function, then locate each subsequent derivative to reach the nth.

Here, the function is given as,

$e^{x} (2x+3)^{3}$.

Then, the first derivative is, $e^{x} (2x+3)^{2} (2x+9)$.

The second derivative is, $(8x^{3} +84x^{2} +246x+207)e^{x}$.

Hence, the 2nd derivative is $(8x^{3} +84x^{2} +246x+207)e^{x}$.

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