Differentiate. y=(sinx)/(x^2)

Name: Problem 25, Chapter 3: Biocalculus Calculus for the Life Sciences
Uploaded: 2020-03-25T22:50:09-08:00
Duration: 49 s
Channel: Amrita Bhasin
Description: Differentiate. y=(sinx)/(x^2)

Key Concepts

Differentiation

Differentiation is the fundamental process in calculus used to compute the rate at which a function changes at any point. It provides a means to analyze and understand the behavior of functions, particularly in terms of slopes of tangents and instantaneous rates of change.

Quotient Rule

The quotient rule is a technique for finding the derivative of a function that is expressed as the ratio of two differentiable functions. It states that if a function is given by f(x)/g(x), its derivative is [g(x)f'(x) - f(x)g'(x)] divided by [g(x)]^2, which helps in handling functions where direct application of basic derivative rules is not sufficient.

Derivative of Trigonometric Functions

The derivatives of trigonometric functions are well-established and crucial in calculus. For instance, the derivative of sin x is cos x, and these relationships enable the differentiation of expressions that include trigonometric functions, playing an important role when such functions are part of more complex expressions.

Power Rule

The power rule is an essential principle in differentiation stating that if a function is in the form x^n, its derivative is n multiplied by x raised to the (n-1) power. This rule simplifies the process of differentiating polynomial terms and is widely applied in conjunction with other rules like the quotient and product rules.

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