Differentiate the function. y=3 e^x+(4)/(√(x))

Name: Problem 15, Chapter 3: Calculus
Uploaded: 2017-10-18T06:58:02-08:00
Duration: 28 s
Channel: Frank Lin
Description: Differentiate the function. y=3 e^x+(4)/(√(x))

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Key Concepts

Differentiation

Differentiation is a fundamental concept in calculus that involves finding the derivative of a function. The derivative represents the rate at which the function's value changes with respect to changes in its input variable, and is defined as the limit of the difference quotient as the change in the input approaches zero.

Exponential Functions

When differentiating exponential functions, particularly the natural exponential function e^x, it is important to recognize that the derivative of e^x is e^x itself. This property makes exponential functions unique and especially useful in various applications of calculus.

Power Rule

The power rule is a key technique in differentiation used for functions of the form x^n, where n is any real number. The rule states that the derivative of x^n is n multiplied by x raised to the power of (n - 1), which is essential for differentiating polynomial and power functions.

Constant Multiple Rule

The constant multiple rule in differentiation states that when a function is multiplied by a constant, the derivative of the function is also multiplied by that constant. This rule simplifies the process of differentiating functions that include constant factors.

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