Question

Find $f^{\prime}(x)$. $f(x)=\left(2-x-3 x^{3}\right)\left(7+x^{5}\right)$

   Find $f^{\prime}(x)$.
$f(x)=\left(2-x-3 x^{3}\right)\left(7+x^{5}\right)$

Calculus Early Transcendentals

Calculus Early Transcendentals

Howard Anton, Irl… 9th Edition

Chapter 2, Problem 6

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Solved by Expert Amy Jiang

08/14/2020

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Mathematically, this is represented as: \[ (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) \] Show more…

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Find $f^{\prime}(x)$. $f(x)=\left(2-x-3 x^{3}\right)\left(7+x^{5}\right)$

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Key Concepts

Differentiation

Differentiation is the process of finding the derivative of a function, which represents the rate of change of the function with respect to one of its variables. It is a fundamental concept in calculus that is used to analyze how functions change and to solve problems in various fields including physics, engineering, and economics.

Product Rule

The product rule is a technique in differentiation used when a function is the product of two or more functions. This rule states that the derivative of a product of functions is equal to the derivative of the first function multiplied by the second function, plus the first function multiplied by the derivative of the second function, and it can be extended to more functions as needed.

Polynomial Differentiation

Polynomial differentiation involves applying basic rules such as the power rule to find the derivative of polynomial functions. The power rule states that the derivative of x^n is n*x^(n-1) for any real number n, and this rule is directly applied to each term of a polynomial, making it a straightforward process compared to differentiating more complex functions.

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