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Given
sin(xy^(3))=y^(3), find
(dy)/(dx) in terms of
x and
y
Answer Attempt 1 out of 2

Given $\sin \left(x y^{3}\right)=y^{3}$ , find $\frac{d y}{d x}$ in terms of $x$ and $y$ $\newline$ Answer Attempt $1$ out of $2$

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Evaluate expression when two complex numbers are given

Full solution

Q. Given

\sin \left(x y^{3}\right)=y^{3}

, find

\frac{d y}{d x}

in terms of

x

and

y

\newline

Answer Attempt

1

out of

2

Differentiate with respect to x: Differentiate both sides of the equation with respect to $x$ . $\newline$ $\frac{d}{dx}[\sin(xy^3)] = \frac{d}{dx}[y^3]$ $\newline$ Using the chain rule on the left side and the power rule on the right side, $\newline$ $\cos(xy^3) \cdot \frac{d}{dx}[xy^3] = 3y^2 \cdot \frac{dy}{dx}$
Apply chain and power rule: Differentiate $xy^3$ with respect to $x$ . $\newline$ $\frac{d}{dx}[xy^3] = y^3 + 3xy^2 \cdot \frac{dy}{dx}$ $\newline$ Here, we used the product rule.

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