Find the derivative of y = 5 sin (-x).


Find the derivative of {eq}y = 5 \sin (-x) {/eq}.


We have a sine function and we have to find its derivative. There are many ways to find the derivative of any function as the product rule, quotient rule, etc. Here we will apply the standard derivative formula.

Answer and Explanation:

$$y = 5 \sin (-x)\\ $$

As we know the following trigonometric identity:

$$\sin (-x)=-\sin x $$

We can write the function as:

$$y=-5\sin x\\ $$

We will use the following derivative formula:

$$\frac{\mathrm{d} }{\mathrm{d} x}\sin x=\cos x\\ y'=-5\cos x $$

Learn more about this topic:

Derivatives: The Formal Definition

from Math 104: Calculus

Chapter 7 / Lesson 5

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