Question

Determine the first derivative (dy/dx) of y= (tan 3x^2)

Second order linear equations
ANSWERED
asked 2021-01-15
Determine the first derivative \(\displaystyle{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}\) of
\(\displaystyle{y}={\left({\tan{{3}}}{x}^{{2}}\right)}\)

Answers (1)

2021-01-16
\(\displaystyle{y}={\tan{{\left({3}{x}^{{2}}\right)}}}\)
\(\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}=\frac{{d}}{{\left.{d}{x}\right.}}{\left({\tan{{\left({3}{x}^{{2}}\right)}}}\right)}\cdot\frac{{d}}{{\left.{d}{x}\right.}}{\left({3}{x}^{{2}}\right)}\)
\(\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={{\sec}^{{2}}{\left({3}{x}{2}\right)}}\cdot{6}{x}={6}{x}\cdot{{\sec}^{{2}}{\left({3}{x}^{{2}}\right)}}\)
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