For the following equation, find (dy)/(dx). y=7x^(5)+2x^(4) Answer: (dy)/(dx)=

Identify function: Identify the function to differentiate. We are given the function y = 7x^(5) + 2x^(4) and we need to find its derivative with respect to x, which is denoted as (dy)/(dx).Apply power rule: Apply the power rule for differentiation. The power rule states that the derivative of x^n with respect to x is n*x^(n-1). We will apply this rule to each term in the function separately.Differentiate first term: Differentiate the first term 7x^(5). Using the power rule, the derivative of 7x^(5) with respect to x is 5 * 7x^(5-1) = 35x^(4).Differentiate second term: Differentiate the second term 2x^(4). Using the power rule, the derivative of 2x^(4) with respect to x is 4 * 2x^(4-1) = 8x^(3).Combine derivatives: Combine the derivatives of both terms to find the overall derivative. (dy)/(dx) = 35x^(4) + 8x^(3).

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For the following equation, find
(dy)/(dx).

y=7x^(5)+2x^(4)
Answer:
(dy)/(dx)=

For the following equation, find $\frac{d y}{d x}$ . $\newline$ $y=7 x^{5}+2 x^{4}$ $\newline$ Answer: $\frac{d y}{d x}=$

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Algebra 1

Multiplication with rational exponents

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Q. For the following equation, find

\frac{d y}{d x}

\newline

y=7 x^{5}+2 x^{4}

\newline

Answer:

\frac{d y}{d x}=

Identify function: Identify the function to differentiate. $\newline$ We are given the function $y = 7x^{5} + 2x^{4}$ and we need to find its derivative with respect to $x$ , which is denoted as $\frac{dy}{dx}$ .
Apply power rule: Apply the power rule for differentiation. $\newline$ The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . We will apply this rule to each term in the function separately.
Differentiate first term: Differentiate the first term $7x^{5}$ . Using the power rule, the derivative of $7x^{5}$ with respect to $x$ is $5 \times 7x^{5-1} = 35x^{4}$ .
Differentiate second term: Differentiate the second term $2x^{4}$ . Using the power rule, the derivative of $2x^{4}$ with respect to $x$ is $4 \times 2x^{4-1} = 8x^{3}$ .
Combine derivatives: Combine the derivatives of both terms to find the overall derivative. $\frac{dy}{dx} = 35x^{4} + 8x^{3}$ .