Question

question 26 - 1 point
find $\frac{dy}{dx}$, where $y$ is defined as a function of $x$ implicitly by the equation below.
$-6x^{4}+2y^{4}=11$
do not include \$\frac{dy}{dx}=$\ in your answer.
provide your answer below:

Explanation:

Step1: Differentiate both sides

Differentiating $-6x^{4}+2y^{4}=11$ with respect to $x$ gives $-24x^{3}+8y^{3}\frac{dy}{dx}=0$.

Step2: Solve for $\frac{dy}{dx}$

$8y^{3}\frac{dy}{dx}=24x^{3}$, so $\frac{dy}{dx}=\frac{24x^{3}}{8y^{3}}=\frac{3x^{3}}{y^{3}}$.

Answer:

$\frac{3x^{3}}{y^{3}}$