Question

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

Derivatives
ANSWERED
asked 2021-04-27
find the indicated derivatives. \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}{\quad\text{if}\quad}{y}={2}{x}^{{{3}}}\)

Answers (1)

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,
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={2}\cdot{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({x}^{{{3}}}\right)}\)
\(\displaystyle={2}\cdot{3}{x}^{{{2}}}\)
\(\displaystyle={6}{x}^{{{2}}}\)
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