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In Exercises $1-18,$ find $d y / d x$ $$y=-10 x+3 \cos x$$

   In Exercises $1-18,$ find $d y / d x$
$$y=-10 x+3 \cos x$$

Calculus

George B. Thomas,… 12th Edition

Chapter 3, Problem 1

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Solved by Expert Patrick Vaughn

07/31/2020

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We want to find the derivative of this function with respect to $x$, which is denoted as $\frac{d y}{d x}$. Show more…

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In Exercises $1-18,$ find $d y / d x$ $$y=-10 x+3 \cos x$$

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Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that involves finding the derivative of a function, which represents the instantaneous rate of change or the slope of the tangent line to the function’s graph at a given point. It is essential for analyzing and understanding the behavior of functions.

Constant Multiple Rule

The constant multiple rule states that the derivative of a constant multiplied by a function is equal to the constant multiplied by the derivative of that function. This rule simplifies the differentiation process when dealing with terms that have constant factors.

Sum Rule

The sum rule in differentiation states that the derivative of the sum of two or more functions is the sum of the derivatives of those functions. This allows for the differentiation of complex functions by breaking them into simpler parts.

Derivative of Trigonometric Functions

Differentiating trigonometric functions involves specific rules, such as the fact that the derivative of the cosine function is the negative sine function. Understanding these rules is important when dealing with functions that include trigonometric components.

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