Question

# find the indicated derivatives. \frac{dy}{dx} if y = 2x^{3}

Derivatives
find the indicated derivatives. $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}{\quad\text{if}\quad}{y}={2}{x}^{{{3}}}$$

2021-04-29
Step 1
We have given, $$\displaystyle{y}={2}{x}^{{{3}}}$$
Step 2
By using the power rule of derivative and constant multiple rules,
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={2}\cdot{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({x}^{{{3}}}\right)}$$
$$\displaystyle={2}\cdot{3}{x}^{{{2}}}$$
$$\displaystyle={6}{x}^{{{2}}}$$