Find f^'(x). f(x)=lnx^2+4 e^x

Name: Problem 21, Chapter 3: Calculus for Business, Economics, Life Sciences, and Social Sciences
Uploaded: 2021-02-22T17:56:48-08:00
Duration: 1 min 30 s
Channel: Gregory Higby
Description: Find f^'(x). f(x)=lnx^2+4 e^x

Key Concepts

Chain Rule

The chain rule is a fundamental method in calculus used to find the derivative of a composite function. It states that if a function is composed of an outer function and an inner function, then its derivative is the derivative of the outer function evaluated at the inner function multiplied by the derivative of the inner function.

Logarithmic Function Differentiation

Differentiating logarithmic functions involves recognizing that for a function of the form ln(g(x)), the derivative is g'(x)/g(x). This technique often requires applying the chain rule when the argument of the logarithm is more complex than simply x.

Exponential Differentiation

The process of differentiating exponential functions, such as e^x, relies on the fact that the derivative of e^x is e^x itself. If the exponent is a function of x, the chain rule must be applied to account for the inner function.

Sum Rule in Differentiation

The sum rule allows us to differentiate a sum of functions by taking the derivative of each function individually and then adding the results. This simplifies the process when dealing with complex functions that are expressed as sums.

Constant Multiple Rule

The constant multiple rule states that the derivative of a constant multiplied by a function is the constant multiplied by the derivative of the function. This rule is used to easily handle terms in an expression that are scaled by constant factors.

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