Question

Derivatives from a table Use the table to find the following derivatives. (TABLE CAN'T COPY) $$\left.\frac{d}{d x}[1.5 f(x)]\right|_{x=2}$$

   Derivatives from a table Use the table to find the following derivatives. (TABLE CAN'T COPY)
$$\left.\frac{d}{d x}[1.5 f(x)]\right|_{x=2}$$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 3, Problem 57

Instant Answer

Solved by Expert Linh Vu

05/27/2020

Step 1

The constant rule of differentiation states that the derivative of a constant times a function is equal to the constant times the derivative of the function. Therefore, we can bring the constant 1.5 outside the derivative. $$\frac{d}{d x}[1.5 f(x)] = 1.5 Show more…

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Derivatives from a table Use the table to find the following derivatives. (TABLE CAN'T COPY) $$\left.\frac{d}{d x}[1.5 f(x)]\right|_{x=2}$$

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Key Concepts

Evaluation of a Derivative at a Point

Evaluating the derivative at a specific point means computing the instantaneous rate of change or the slope of the function at that precise coordinate. This concept is crucial for applications such as finding tangents to curves and analyzing function behavior at given points.

Derivative

The derivative of a function quantifies the rate at which the function’s value changes with respect to changes in its input. It represents the slope of the tangent line to the function at any given point and is foundational to understanding rates of change in calculus.

Constant Multiple Rule

The Constant Multiple Rule in differentiation states that if a function is scaled by a constant, its derivative is simply that same constant multiplied by the derivative of the original function. This rule allows one to easily compute derivatives of functions that have been multiplied by a constant factor.

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