-apc.2.2.03 trig product rule

In summary, the "-apc.2.2.03 trig product rule" is a mathematical rule used to find the derivative of a product of two trigonometric functions. It is important because it allows us to find the derivative in equations where the product of trigonometric functions is present. To use the trig product rule, you need to first identify the product of the two functions and then use the formula (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) to find the derivative. The rule can be applied to any product of two differentiable trigonometric functions, but it has limitations as it cannot be used for products of three or more functions and the functions must
  • #1

karush

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If $y=x \sin x,$ then $\dfrac{dy}{dx}=$

$a.\quad\sin{x}+\cos{x}$
$b.\quad\sin{x}+x\cos{x}$
$c.\quad\sin{x}+\cos{x}$
$d.\quad x(\sin{x}+\cos{x})$
$e.\quad x(\sin{x}-\cos{x})$
well just by looking at it because $dx(x) = 1$
elimanates all the options besides b

$1\cdot \sin (x)+\cos (x)x$ or $\sin (x)+x\cos (x)$
otherwise the gymnastics of the product rule
$uv'+u'v$
 
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  • #2
Yup. You got it.

-Dan
 

1. What is the product rule in trigonometry?

The product rule in trigonometry is a formula used to find the derivative of a product of two functions. It states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function, plus the second function multiplied by the derivative of the first function.

2. How do you use the product rule in trigonometry?

To use the product rule in trigonometry, you first identify the two functions that are being multiplied together. Then, you take the derivative of each individual function. Finally, you plug these derivatives into the product rule formula to find the derivative of the product of the two functions.

3. Can the product rule be applied to more than two functions?

Yes, the product rule can be applied to any number of functions that are being multiplied together. For example, if you have three functions being multiplied, the product rule formula would include the derivatives of all three functions.

4. What are some common mistakes when using the product rule in trigonometry?

One common mistake when using the product rule in trigonometry is forgetting to take the derivative of each individual function before plugging them into the formula. Another mistake is mixing up the order of the functions when plugging them into the formula.

5. How is the product rule related to the chain rule in calculus?

The product rule is a special case of the chain rule in calculus. The chain rule is used to find the derivative of a composite function, where one function is nested inside another. The product rule is a specific application of the chain rule when the composite function is a product of two individual functions.

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