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

Identify function: Identify the function to differentiate. We are given the function y=4x^(5)+4x-7 and we need to find its derivative with respect to x, which is denoted as (dy)/(dx).Apply power rule: Apply the power rule to each term. 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 4x^(5). Using the power rule, the derivative of 4x^(5) with respect to x is 5*4x^(5-1) = 20x^(4).Differentiate second term: Differentiate the second term 4x. The derivative of 4x with respect to x is 4, since the power of x is 1 and 1*4x^(1-1) = 4*1 = 4.Differentiate constant term: Differentiate the constant term -7. The derivative of a constant is 0, so the derivative of -7 with respect to x is 0.Combine derivatives: Combine the derivatives of all terms to find (dy)/(dx). (dy)/(dx) = 20x^(4) + 4 + 0 Simplify the expression by removing the 0. (dy)/(dx) = 20x^(4) + 4

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

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

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

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Algebra 2

Find the vertex of the transformed function

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Q. For the following equation, find

\frac{d y}{d x}

\newline

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

\newline

Answer:

\frac{d y}{d x}=

Identify function: Identify the function to differentiate. $\newline$ We are given the function $y=4x^{5}+4x-7$ 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 to each term. $\newline$ 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 $4x^{5}$ . Using the power rule, the derivative of $4x^{5}$ with respect to $x$ is $5\cdot 4x^{5-1} = 20x^{4}$ .
Differentiate second term: Differentiate the second term $4x$ . The derivative of $4x$ with respect to $x$ is $4$ , since the power of $x$ is $1$ and $1\times4x^{1-1} = 4\times1 = 4$ .
Differentiate constant term: Differentiate the constant term $-7$ . The derivative of a constant is $0$ , so the derivative of $-7$ with respect to $x$ is $0$ .
Combine derivatives: Combine the derivatives of all terms to find $\frac{dy}{dx}$ . $\frac{dy}{dx} = 20x^{4} + 4 + 0$ Simplify the expression by removing the $0$ . $\frac{dy}{dx} = 20x^{4} + 4$