Differentiate the function. z=(A)/(y^10)+B e^y

Name: Problem 25, Chapter 3: Calculus
Uploaded: 2021-08-28T23:05:40-08:00
Duration: 1 min 1 s
Channel: Ma. Theresa Alin
Description: Differentiate the function. z=(A)/(y^10)+B e^y

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Key Concepts

Power Rule

The power rule is used to differentiate functions of the form y^n, where n is any real number. It states that the derivative of y^n with respect to y is n * y^(n-1). This rule is essential when handling terms that can be expressed as powers of y, including those rewritten with negative exponents.

Exponential Function Differentiation

Differentiation of the exponential function, particularly e^(y), is straightforward since the derivative of e^(y) with respect to y is simply e^(y). This property makes the exponential function one of the easiest to differentiate and is widely used in various applications.

Constant Multiple Rule

The constant multiple rule indicates that when differentiating a function multiplied by a constant, the constant factor is preserved, and only the differentiation of the function itself is required. This rule simplifies the process by allowing the constant factors to be carried along throughout the differentiation process.

Sum Rule

The sum rule in differentiation states that the derivative of a sum of functions is equal to the sum of the derivatives of each individual function. This principle allows complex expressions to be broken down into simpler parts, each of which can be differentiated separately.

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