If -2y^(3)=1+x^(3) then find (dy)/(dx) in terms of x and y. Answer: (dy)/(dx)=

Write Equation: Write down the given equation. The given equation is -2y^(3) = 1 + x^(3).Differentiate with Respect: Differentiate both sides of the equation with respect to x. To find (dy)/(dx), we need to differentiate both sides of the equation with respect to x. Remember that y is a function of x, so when differentiating terms with y, we use the chain rule. d/dx(-2y^(3)) = d/dx(1 + x^(3))Apply Chain and Power Rule: Apply the chain rule to the left side and the power rule to the right side. Using the chain rule on the left side, we get -6y^(2) * (dy)/(dx). On the right side, the derivative of 1 is 0, and the derivative of x^(3) is 3x^(2). -6y^(2) * (dy)/(dx) = 0 + 3x^(2)Solve for (dy)/(dx): Solve for (dy)/(dx). To solve for (dy)/(dx), we divide both sides of the equation by -6y^(2). (dy)/(dx) = 3x^(2) / (-6y^(2))Simplify Expression: Simplify the expression for (dy)/(dx). We can simplify the fraction by dividing the numerator and the denominator by 3. (dy)/(dx) = x^(2) / (-2y^(2))

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
-2y^(3)=1+x^(3) then find
(dy)/(dx) in terms of
x and
y.
Answer:
(dy)/(dx)=

If $-2 y^{3}=1+x^{3}$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ . $\newline$ Answer: $\frac{d y}{d x}=$

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate exponential functions

Full solution

Q. If

-2 y^{3}=1+x^{3}

then find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer:

\frac{d y}{d x}=

Write Equation: Write down the given equation. $\newline$ The given equation is $-2y^{3} = 1 + x^{3}$ .
Differentiate with Respect: Differentiate both sides of the equation with respect to $x$ . To find $\frac{dy}{dx}$ , we need to differentiate both sides of the equation with respect to $x$ . Remember that $y$ is a function of $x$ , so when differentiating terms with $y$ , we use the chain rule. $\frac{d}{dx}(-2y^{3}) = \frac{d}{dx}(1 + x^{3})$
Apply Chain and Power Rule: Apply the chain rule to the left side and the power rule to the right side. $\newline$ Using the chain rule on the left side, we get $-6y^{2} \cdot \frac{dy}{dx}$ . On the right side, the derivative of $1$ is $0$ , and the derivative of $x^{3}$ is $3x^{2}$ . $\newline$ $-6y^{2} \cdot \frac{dy}{dx} = 0 + 3x^{2}$
Solve for $(\frac{dy}{dx}):$ Solve for $(\frac{dy}{dx})$ . To solve for $(\frac{dy}{dx})$ , we divide both sides of the equation by $-6y^{2}$ . $(\frac{dy}{dx}) = \frac{3x^{2}}{-6y^{2}}$
Simplify Expression: Simplify the expression for $(\frac{dy}{dx})$ . We can simplify the fraction by dividing the numerator and the denominator by $3$ . $(\frac{dy}{dx}) = \frac{x^{2}}{-2y^{2}}$