Given y=3sin(x), find (dy)/(dx). Answer: (dy)/(dx)=

Identify Function: Identify the function to differentiate. We are given the function y = 3sin(x), and we need to find its derivative with respect to x, which is denoted as (dy)/(dx).Apply Differentiation Rule: Apply the differentiation rule for sine. The derivative of sin(x) with respect to x is cos(x). Since we have a constant multiple of 3 in front of sin(x), we use the constant multiple rule which states that the derivative of a constant times a function is the constant times the derivative of the function.Calculate Derivative: Calculate the derivative. Using the rule from Step 2, we find the derivative of y = 3sin(x) with respect to x. (dy)/(dx) = 3 * (d/dx)(sin(x)) (dy)/(dx) = 3 * cos(x)

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Given
y=3sin(x), find
(dy)/(dx).
Answer:
(dy)/(dx)=

Given $y=3 \sin (x)$ , find $\frac{d y}{d x}$ . $\newline$ Answer: $\frac{d y}{d x}=$

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Q. Given

y=3 \sin (x)

, find

\frac{d y}{d x}

\newline

Answer:

\frac{d y}{d x}=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $y = 3\sin(x)$ , and we need to find its derivative with respect to $x$ , which is denoted as $\frac{dy}{dx}$ .
Apply Differentiation Rule: Apply the differentiation rule for sine. $\newline$ The derivative of $\sin(x)$ with respect to $x$ is $\cos(x)$ . Since we have a constant multiple of $3$ in front of $\sin(x)$ , we use the constant multiple rule which states that the derivative of a constant times a function is the constant times the derivative of the function.
Calculate Derivative: Calculate the derivative. $\newline$ Using the rule from Step $2$ , we find the derivative of $y = 3\sin(x)$ with respect to $x$ . $\newline$ $\frac{dy}{dx} = 3 \cdot \frac{d}{dx}(\sin(x))$ $\newline$ $\frac{dy}{dx} = 3 \cdot \cos(x)$