Find (d)/(dx)(sin 7x) Answer:

Identify Chain Rule: We need to find the derivative of sin(7x) with respect to x. According to the chain rule, the derivative of sin(u) with respect to x is cos(u) times the derivative of u with respect to x, where u is a function of x. In this case, u = 7x.Find Derivative of u: First, we find the derivative of u = 7x with respect to x. The derivative of 7x with respect to x is 7, because the derivative of x is 1 and 7 is a constant.Apply Chain Rule: Now, we apply the chain rule. The derivative of sin(7x) with respect to x is cos(7x) times the derivative of 7x with respect to x, which we found to be 7.Final Derivative: Therefore, the derivative of sin(7x) with respect to x is 7 * cos(7x).

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Find $\frac{d}{d x}(\sin 7 x)$ $\newline$ Answer:

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Algebra 2

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Q. Find

\frac{d}{d x}(\sin 7 x)

\newline

Answer:

Identify Chain Rule: We need to find the derivative of $\sin(7x)$ with respect to $x$ . According to the chain rule, the derivative of $\sin(u)$ with respect to $x$ is $\cos(u)$ times the derivative of $u$ with respect to $x$ , where $u$ is a function of $x$ . In this case, $u = 7x$ .
Find Derivative of u: First, we find the derivative of $u = 7x$ with respect to $x$ . The derivative of $7x$ with respect to $x$ is $7$ , because the derivative of $x$ is $1$ and $7$ is a constant.
Apply Chain Rule: Now, we apply the chain rule. The derivative of $\sin(7x)$ with respect to $x$ is $\cos(7x)$ times the derivative of $7x$ with respect to $x$ , which we found to be $7$ .
Final Derivative: Therefore, the derivative of $\sin(7x)$ with respect to $x$ is $7 \cdot \cos(7x)$ .