find the derivative of sin²x cosx
English Meaning & Definitions
To perform the mathematical operation of differentiation on the function f(x) = sin²(x)cos(x) using the product and chain rules, resulting in the expression 2sin(x)cos²(x) - sin³(x).
- “To find the derivative of sin²x cosx, you must treat sin²x as the first function and cosx as the second.”
- “The final step to find the derivative of sin²x cosx involves simplifying the expression using trigonometric identities.”
English Synonyms & Near Equivalents
English Antonyms & Opposites
Comprehensive Thesaurus Breakdown
Compare formal, informal, literary synonyms and register nuances for “find the derivative of sin²x cosx”.
The term 'derivative' stems from the Latin 'derivare', meaning 'to draw off' or 'to lead away'. The trigonometric terms 'sine' and 'cosine' originate from the Sanskrit 'jyā' (chord), translated into Arabic as 'jiba', then misread as 'jaib' (fold/bay), which Latin scholars translated as 'sinus'. This specific mathematical query involves applying the Product Rule and Chain Rule, foundational concepts developed by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century.
Product Rule: 'Left d-Right plus Right d-Left'
Frequently Asked Questions About “find the derivative of sin²x cosx”
1. What is the meaning of “find the derivative of sin²x cosx” in English?
In English, find the derivative of sin²x cosx (verb) is defined as: “To perform the mathematical operation of differentiation on the function f(x) = sin²(x)cos(x) using the product and chain rules, resulting in the expression 2sin(x)cos²(x) - sin³(x).”.
2. How do you use “find the derivative of sin²x cosx” in a sentence?
“To find the derivative of sin²x cosx, you must treat sin²x as the first function and cosx as the second.”
3. What are English synonyms of “find the derivative of sin²x cosx”?
4. What is the etymology and word origin of “find the derivative of sin²x cosx”?
The term 'derivative' stems from the Latin 'derivare', meaning 'to draw off' or 'to lead away'. The trigonometric terms 'sine' and 'cosine' originate from the Sanskrit 'jyā' (chord), translated into Arabic as 'jiba', then misread as 'jaib' (fold/bay), which Latin scholars translated as 'sinus'. This specific mathematical query involves applying the Product Rule and Chain Rule, foundational concepts developed by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century.
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A specific duration of time equal to one hour and forty-six minutes and twelve seconds.
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