Find (d)/(dg)(g^(4)+3sin g) Answer:

Identify function: Identify the function to differentiate. We are given the function f(g) = g^4 + 3sin(g), and we need to find its derivative with respect to g.Apply power rule: Apply the power rule to the first term. The power rule states that the derivative of g^n with respect to g is n*g^(n-1). Therefore, the derivative of g^4 with respect to g is 4*g^(4-1) or 4g^3.Apply sine rule: Apply the derivative rule for the sine function to the second term. The derivative of sin(g) with respect to g is cos(g). Therefore, the derivative of 3sin(g) with respect to g is 3cos(g).Combine derivatives: Combine the derivatives of both terms. The derivative of the function f(g) = g^4 + 3sin(g) with respect to g is the sum of the derivatives of its individual terms. So, we combine the results from Step 2 and Step 3 to get the final derivative. The derivative is 4g^3 + 3cos(g).

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Find $\frac{d}{d g}\left(g^{4}+3 \sin g\right)$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Find

\frac{d}{d g}\left(g^{4}+3 \sin g\right)

\newline

Answer:

Identify function: Identify the function to differentiate. $\newline$ We are given the function $f(g) = g^4 + 3\sin(g)$ , and we need to find its derivative with respect to $g$ .
Apply power rule: Apply the power rule to the first term. $\newline$ The power rule states that the derivative of $g^n$ with respect to $g$ is $n\cdot g^{(n-1)}$ . Therefore, the derivative of $g^4$ with respect to $g$ is $4\cdot g^{(4-1)}$ or $4g^3$ .
Apply sine rule: Apply the derivative rule for the sine function to the second term. $\newline$ The derivative of $\sin(g)$ with respect to $g$ is $\cos(g)$ . Therefore, the derivative of $3\sin(g)$ with respect to $g$ is $3\cos(g)$ .
Combine derivatives: Combine the derivatives of both terms. $\newline$ The derivative of the function $f(g) = g^4 + 3\sin(g)$ with respect to $g$ is the sum of the derivatives of its individual terms. So, we combine the results from Step $2$ and Step $3$ to get the final derivative. $\newline$ The derivative is $4g^3 + 3\cos(g)$ .