For the following equation, evaluate (dy)/(dx) when x=-1. y=2x^(5)+2x^(3) Answer:

Apply Power Rule: To find the derivative of y with respect to x, we need to apply the power rule of differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).Differentiate 2x^5: Differentiate the first term 2x^(5) using the power rule: The derivative is 5 * 2x^(5-1) = 10x^(4).Differentiate 2x^3: Differentiate the second term 2x^(3) using the power rule: The derivative is 3 * 2x^(3-1) = 6x^(2).Combine Derivatives: Combine the derivatives of both terms to get the overall derivative (dy)/(dx): (dy)/(dx) = 10x^(4) + 6x^(2).Substitute x = -1: Now, substitute x = -1 into the derivative to evaluate (dy)/(dx) at x = -1: (dy)/(dx) = 10(-1)^(4) + 6(-1)^(2).Calculate Powers: Calculate the powers of -1: (-1)^(4) = 1 and (-1)^(2) = 1.Substitute Values: Substitute the values back into the expression: (dy)/(dx) = 10(1) + 6(1) = 10 + 6.Find Final Value: Add the numbers to find the value of (dy)/(dx) when x = -1: (dy)/(dx) = 10 + 6 = 16.

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For the following equation, evaluate
(dy)/(dx) when
x=-1.

y=2x^(5)+2x^(3)
Answer:

For the following equation, evaluate $\frac{d y}{d x}$ when $x=-1$ . $\newline$ $y=2 x^{5}+2 x^{3}$ $\newline$ Answer:

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Algebra 1

Evaluate a function: plug in an expression

Full solution

Q. For the following equation, evaluate

\frac{d y}{d x}

when

x=-1

\newline

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

\newline

Answer:

Apply Power Rule: To find the derivative of $y$ with respect to $x$ , we need to apply the power rule of differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ .
Differentiate $2x^5$ : Differentiate the first term $2x^{5}$ using the power rule: The derivative is $5 \times 2x^{5-1} = 10x^{4}$ .
Differentiate $2x^3$ : Differentiate the second term $2x^{3}$ using the power rule: The derivative is $3 \times 2x^{3-1} = 6x^{2}$ .
Combine Derivatives: Combine the derivatives of both terms to get the overall derivative $\frac{dy}{dx}$ : $\frac{dy}{dx} = 10x^{4} + 6x^{2}$ .
Substitute $x = -1$ : Now, substitute $x = -1$ into the derivative to evaluate $\frac{dy}{dx}$ at $x = -1$ : $\frac{dy}{dx} = 10(-1)^{4} + 6(-1)^{2}$ .
Calculate Powers: Calculate the powers of $-1$ : $(-1)^{4} = 1$ and $(-1)^{2} = 1$ .
Substitute Values: Substitute the values back into the expression: $(\frac{dy}{dx}) = 10(1) + 6(1) = 10 + 6$ .
Find Final Value: Add the numbers to find the value of $(dy)/(dx)$ when $x = -1$ : $(dy)/(dx) = 10 + 6 = 16$ .