For the following equation, evaluate (dy)/(dx) when x=-1. y=4x^(5)+3 Answer:

Identify Equation and Derivative: Identify the equation and the derivative we need to find. We are given the equation y = 4x^(5) + 3 and we need to find the derivative of y with respect to x, which is denoted as (dy)/(dx).Differentiate with Respect to x: Differentiate the equation with respect to x. To find (dy)/(dx), we need to differentiate each term of the equation y = 4x^(5) + 3 with respect to x. The derivative of 4x^(5) with respect to x is 20x^(4) (using the power rule: d/dx [x^n] = nx^(n-1)). The derivative of a constant, like 3, is 0. So, (dy)/(dx) = 20x^(4) + 0, which simplifies to (dy)/(dx) = 20x^(4).Evaluate at x = -1: Evaluate the derivative at x = -1. Now that we have the derivative, we can substitute x = -1 into (dy)/(dx) = 20x^(4) to find the value of the derivative at that point. (dy)/(dx) at x = -1 is 20(-1)^(4). Since (-1)^(4) is 1, this simplifies to (dy)/(dx) at x = -1 is 20 * 1, which is 20.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

y=4x^(5)+3
Answer:

For the following equation, evaluate $\frac{d y}{d x}$ when $x=-1$ . $\newline$ $y=4 x^{5}+3$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

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=4 x^{5}+3

\newline

Answer:

Identify Equation and Derivative: Identify the equation and the derivative we need to find. $\newline$ We are given the equation $y = 4x^{5} + 3$ and we need to find the derivative of $y$ with respect to $x$ , which is denoted as $\frac{dy}{dx}$ .
Differentiate with Respect to x: Differentiate the equation with respect to x. $\newline$ To find $(dy)/(dx)$ , we need to differentiate each term of the equation $y = 4x^{5} + 3$ with respect to x. $\newline$ The derivative of $4x^{5}$ with respect to x is $20x^{4}$ (using the power rule: $d/dx [x^n] = nx^{(n-1)}$ ). $\newline$ The derivative of a constant, like $3$ , is $0$ . $\newline$ So, $(dy)/(dx) = 20x^{4} + 0$ , which simplifies to $(dy)/(dx) = 20x^{4}$ .
Evaluate at $x = -1$ : Evaluate the derivative at $x = -1$ . $\newline$ Now that we have the derivative, we can substitute $x = -1$ into $\frac{dy}{dx} = 20x^{4}$ to find the value of the derivative at that point. $\newline$ $\frac{dy}{dx}$ at $x = -1$ is $20(-1)^{4}$ . $\newline$ Since $(-1)^{4}$ is $1$ , this simplifies to $\frac{dy}{dx}$ at $x = -1$ is $x = -1$ $1$ , which is $x = -1$ $2$ .