For the following equation, find (dy)/(dx). y=-5x^(5)+5x^(3)+2x Answer: (dy)/(dx)=

Identify Function: Identify the function to differentiate. The function given is y = -5x^5 + 5x^3 + 2x. We need to find the derivative of this function with respect to x, which is denoted as (dy)/(dx).Apply Power Rule: Apply the power rule to each term of the function. 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 of the function separately.Differentiate First Term: Differentiate the first term -5x^5. Using the power rule, the derivative of -5x^5 with respect to x is -5 * 5x^(5-1) = -25x^4.Differentiate Second Term: Differentiate the second term 5x^3. Using the power rule, the derivative of 5x^3 with respect to x is 5 * 3x^(3-1) = 15x^2.Differentiate Third Term: Differentiate the third term 2x. Using the power rule, the derivative of 2x with respect to x is 2 * 1x^(1-1) = 2x^0 = 2.Combine Derivatives: Combine the derivatives of all terms to find (dy)/(dx). (dy)/(dx) = -25x^4 + 15x^2 + 2.

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

y=-5x^(5)+5x^(3)+2x
Answer:
(dy)/(dx)=

For the following equation, find $\frac{d y}{d x}$ . $\newline$ $y=-5 x^{5}+5 x^{3}+2 x$ $\newline$ Answer: $\frac{d y}{d x}=$

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Algebra 2

Evaluate exponential functions

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Q. For the following equation, find

\frac{d y}{d x}

\newline

y=-5 x^{5}+5 x^{3}+2 x

\newline

Answer:

\frac{d y}{d x}=

Identify Function: Identify the function to differentiate. $\newline$ The function given is $y = -5x^5 + 5x^3 + 2x$ . We need to find the derivative of this function with respect to $x$ , which is denoted as $\frac{dy}{dx}$ .
Apply Power Rule: Apply the power rule to each term of the function. $\newline$ 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 of the function separately.
Differentiate First Term: Differentiate the first term $-5x^5$ . Using the power rule, the derivative of $-5x^5$ with respect to $x$ is $-5 \times 5x^{5-1} = -25x^4$ .
Differentiate Second Term: Differentiate the second term $5x^3$ . Using the power rule, the derivative of $5x^3$ with respect to $x$ is $5 \times 3x^{3-1} = 15x^2$ .
Differentiate Third Term: Differentiate the third term $2x$ . Using the power rule, the derivative of $2x$ with respect to $x$ is $2 \times 1x^{1-1} = 2x^0 = 2$ .
Combine Derivatives: Combine the derivatives of all terms to find $(\frac{dy}{dx})$ . $\frac{dy}{dx} = -25x^4 + 15x^2 + 2$ .