# derivative of 1 - sin(x)

#### Understand the Problem

The question is asking for the derivative of the function 1 - sin(x). To solve this, we will apply basic differentiation rules, particularly the derivative of a constant and the derivative of the sine function.

$-\cos(x)$

The derivative of $1 - \sin(x)$ is $-\cos(x)$

#### Steps to Solve

1. Differentiate the constant term 1

The derivative of any constant is 0.

$$\frac{d}{dx}[1] = 0$$

1. Differentiate the sine function sin(x)

The derivative of $\sin(x)$ is $\cos(x)$.

$$\frac{d}{dx} [\sin(x)] = \cos(x)$$

1. Apply the minus sign

Since we are differentiating $1 - \sin(x)$, we account for the negative sign before the sine function.

$$\frac{d}{dx} [1 - \sin(x)] = 0 - \cos(x) = -\cos(x)$$

The derivative of $1 - \sin(x)$ is $-\cos(x)$

A common mistake might be to forget applying the minus sign when differentiating $\sin(x)$, or to erroneously assume that the derivative of $1$ is not $0$.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://quizgecko.com/q/derivative-of-1-sinx-iud87", "fetch_time": 1726573463000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2024-38/segments/1725700651773.64/warc/CC-MAIN-20240917104423-20240917134423-00440.warc.gz", "warc_record_offset": 430477959, "warc_record_length": 33515, "token_count": 275, "char_count": 962, "score": 4.5625, "int_score": 5, "crawl": "CC-MAIN-2024-38", "snapshot_type": "latest", "language": "en", "language_score": 0.8450146913528442, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00018-of-00064.parquet"}