Question
Find \( \frac{d y}{d x} \) by implicit differentiation. \[ 9 x^{3}+x^{2} y-x y^{3}=5 \] Step 1 To find \( \frac{d y}{d x}=y^{\prime} \) for \( 9 x^{3}+x^{2} y-x y^{3}=5 \), we differentiate both sides of the equation with respect to \( x \) to create the following equation. \[ \frac{d}{d x}\left[9 x^{3}+x^{2} y-x y^{3}\right]=\frac{d}{d x}[5] \] On the right-hand side, we have the following. \( \frac{d}{d x}[5]= \) ?
Ask by Murphy Lowe. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\frac{d}{dx}[5] = 0
\]
Solution
\[
\frac{d}{dx}[5] = 0
\]
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Simplify this solution Mind Expander
The right-hand side simplifies to \( 0 \), since the derivative of a constant (in this case, \( 5 \)) is always \( 0 \). So, you would write: \[ \frac{d}{d x}[5] = 0. \] Now, you can move on to the left-hand side and apply the product rule and chain rule as needed! Keep going, and have fun with the derivatives!
