Question

Find the derivative of $f\left(x\right)$
$f\left(x\right)=\tan (4+2x)$

• A. $f^{\prime }\left(x\right)={\sec }^2(4+2x)$
• B. $f^{\prime }\left(x\right)=(4+2x){\sec }^2(4+2x)$
• C. $f^{\prime }\left(x\right)=2$
• D. $f^{\prime }\left(x\right)=2{\sec }^2(4+2x)$

Answer 1

The correct option is D $f^{\prime }\left(x\right)=2{\sec }^2(4+2x)$

$f\left(x\right)=\tan (4+2x)$
Using chain rule,
$\frac{d}{dx}g\left(h\right(x\left)\right)=g^{\prime }\left(h\right(x\left)\right)h^{\prime }\left(x\right)$
$\frac{df\left(x\right)}{dx}={\sec }^2(4+2x).2$
$f^{\prime }\left(x\right)=2{\sec }^2(4+2x)$