Calc BC derivative problem with trig and double angle -- Help please

In summary, to find the derivative of f(x) = 8^(sin^2(3x)), we can use the double angle formula for trig functions and the equation y=a^u then y' = ln a * a^u * du. Simplifying the derivative, we get f'(x) = ln 8 * 8^(sin^2(3x)) * 3sin6x, where the 3sin6x comes from taking the derivative of sin^2(3x) and converting it from 6sin3xcos3x to 3sin6x. However, it is unclear how the teacher wanted the answer to only have one trig function.
  • #1
jessieb128
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Homework Statement


Find f'(x) if f(x) = 8^(sin^2(3x))
Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it.

Homework Equations


if y=a^u then y' = ln a * a^u * du
sin(2x) = 2sinxcosx

The Attempt at a Solution


We're only on the second chapter so I'm not sure if we really need the first equation I gave, which is from the fifth chapter (but I'm in BC so maybe she expects us to know it already?). Still, using that equation I got f'(x) = ln 8 * 8^(sin^2(3x)) * 3sin6x

The 3sin6x came from when I took the derivative of sin^2(3x) and converted it from 6sin3xcos3x to 3sin6x

But I don't know how my teacher (an online teacher) wanted the answer to only have one trig function? Did I mess up somewhere?
 
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  • #2
In terms of sin2θ, cos(2θ)=??
 

FAQ: Calc BC derivative problem with trig and double angle -- Help please

1. What is the purpose of using trigonometric functions in calculus?

Trigonometric functions allow us to model and analyze real-world phenomena that involve angles and periodic behavior, making them useful tools in many areas of science and engineering.

2. How do you solve a calculus problem involving a double angle?

To solve a problem involving a double angle, we can use the double angle identities to rewrite the function in terms of a single angle, making it easier to take the derivative and evaluate the problem.

3. Can you explain the chain rule in relation to trigonometric functions?

The chain rule states that when we have a function within a function, we must multiply the derivative of the outer function by the derivative of the inner function. When dealing with trigonometric functions, we must also consider the derivative of the angle inside the function.

4. What is the derivative of a trigonometric function?

The derivative of a trigonometric function depends on the specific function being used. For example, the derivative of sine is cosine, while the derivative of cosine is negative sine.

5. How do you know when to use the product rule or quotient rule in a calculus problem?

The product rule is used when we have a function that is the product of two functions, while the quotient rule is used when we have a fraction with two functions in the numerator and denominator. In general, we use the product rule when differentiating two functions that are being multiplied, and the quotient rule when differentiating two functions that are being divided.

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