Find the differential $$ d y $$ of the given function. $$ y=10 x^{4 / 5} $$ $$ d y=\square $$

Question

UpStudy AI · Accepted Answer

Let 
$$
y = 10 x^{\frac{4}{5}}.
$$

**Step 1.** Compute the derivative:
$$
\frac{dy}{dx} = 10 \cdot \frac{4}{5} x^{\frac{4}{5}-1}.
$$

**Step 2.** Simplify the constant:
$$
10 \cdot \frac{4}{5} = 8.
$$
So,
$$
\frac{dy}{dx} = 8 x^{\frac{4}{5}-1}.
$$

**Step 3.** Subtract the exponents:
$$
\frac{4}{5} - 1 = \frac{4}{5} - \frac{5}{5} = -\frac{1}{5}.
$$
Thus,
$$
\frac{dy}{dx} = 8 x^{-\frac{1}{5}}.
$$

**Step 4.** Write the differential $$dy$$:
$$
dy = 8 x^{-\frac{1}{5}} \, dx.
$$

The differential is 
$$
dy = 8 x^{-\frac{1}{5}} \, dx.
$$
$$ dy = 8 x^{-\frac{1}{5}} \, dx $$

Find the differential of the given function.