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bobsmith76
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Homework Statement
differentiate f(x)= x sin x
Homework Equations
The Attempt at a Solution
The answer is x cos x + (sin x) * 1
I thought the derivative of sine was cosine. So why isn't the answer x cos x?
The derivative of f(x) = x sin x is given by the product rule: f'(x) = x cos x + sin x.
To find the derivative of a product of two functions, you can use the product rule: (f(x)g(x))' = f'(x)g(x) + f(x)g'(x).
Yes, the derivative of f(x) = x sin x can be simplified to f'(x) = x cos x + sin x.
The derivative of f(x) = x sin x represents the instantaneous rate of change or slope of the function at a specific point. It is also useful in finding critical points, which are important in graphing and optimization problems.
The derivative of f(x) = x sin x can be used in physics to calculate the velocity of an object that is moving with simple harmonic motion, such as a pendulum. It can also be used in engineering to model and analyze systems with periodic motion, such as springs and circuits.