Let f(x)=7sin(x)+2cos(x)
Find the dirivative

To find the derivative of the function \( f(x) = 7\sin(x) + 2\cos(x) \), we will apply the basic rules of differentiation for sine and cosine functions.

The derivatives of the basic trigonometric functions are:
- \( \frac{d}{dx} \sin(x) = \cos(x) \)
- \( \frac{d}{dx} \cos(x) = -\sin(x) \)

Now, differentiate each term in the function \( f(x) \):

\[
\frac{d}{dx} [7\sin(x)] = 7\cos(x)
\]
\[
\frac{d}{dx} [2\cos(x)] = -2\sin(x)
\]

Thus, the derivative of \( f(x) \) is:

\[
f'(x) = 7\cos(x) - 2\sin(x)
\]

### Final Answer:
\[
f'(x) = 7\cos(x) - 2\sin(x)
\]

Do you need any further details or clarifications? 

Here are five related questions to expand your understanding:
1. What is the second derivative of \( f(x) \)?
2. How would you find the critical points of \( f(x) \)?
3. Can you integrate \( f(x) = 7\sin(x) + 2\cos(x) \)?
4. What is the amplitude of the function \( f(x) \)?
5. How would you sketch the graph of \( f(x) \)?

**Tip**: When differentiating trigonometric functions, always remember the standard derivatives of sine and cosine.

Let f(x) = 7sin(x) + 2cos(x). Find the derivative.

Learn how to find the derivative of the function f(x) = 7sin(x) + 2cos(x). This solution covers key calculus concepts such as the differentiation of sine and cosine functions and includes a step-by-step process suitable for students in Grades 11-12 or college-level calculus.

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