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markosheehan
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can someone go through the steps how to differentiate (1+sin²x)³
It's multiple uses of the chain rule:markosheehan said:can someone go through the steps how to differentiate (1+sin²x)³
To differentiate (1+sin²x)³, you can use the chain rule and the power rule. First, you would multiply the exponent ³ to each term inside the parentheses, resulting in (1+sin²x)³. Then, you would use the chain rule to differentiate the term inside the parentheses, which would be 2sinx(cosx). Finally, you would use the power rule to differentiate the outer exponent, resulting in the final answer of 3(1+sin²x)²(2sinx)(cosx).
Differentiating (1+sin²x)³ allows us to find the derivative of this function, which is useful in many areas of science such as physics, engineering, and economics. The derivative represents the rate of change of a function at a specific point, which can help us analyze the behavior of the original function.
A step-by-step guide provides a systematic approach to solving a problem, making it easier for individuals to understand and follow the steps. In the case of differentiating (1+sin²x)³, a step-by-step guide helps to break down the process into smaller, more manageable steps, allowing for a better understanding of the concept.
Yes, there are other methods for differentiating (1+sin²x)³, such as using the product rule or the quotient rule. However, for this specific function, using the chain rule and the power rule is the most efficient and straightforward approach.
Differentiating (1+sin²x)³ can be applied in various real-life situations, such as in physics to calculate the velocity of an object, in economics to analyze the rate of change of a company's profit, or in engineering to determine the slope of a curved structure. It is a fundamental concept in calculus that has many practical applications in different fields of science and technology.