Find the derivative using the appropriate rule or combination of rules. $$ y= an \left(x^{2}+18 x ight) $$ $$ y^{\prime}=\square $$

Question

Find the derivative using the appropriate rule or combination of rules. $$ y=	an \left(x^{2}+18 xight) $$ $$ y^{\prime}=\square $$

UpStudy AI · Accepted Answer

Let $$ u(x) = x^2 + 18x $$. Then, the function becomes

$$
y = \tan(u(x))
$$

Using the chain rule, the derivative is

$$
y' = \sec^2(u(x)) \cdot u'(x)
$$

First, find $$ u'(x) $$:

$$
u'(x) = \frac{d}{dx}(x^2+18x) = 2x + 18
$$

Thus, substituting back:

$$
y' = \sec^2(x^2+18x) \cdot (2x+18)
$$
$$ y' = (2x + 18) \sec^2(x^2 + 18x) $$

Find the derivative using the appropriate rule or combination of rules. \( y=\tan \left(x^{2}+18 x\right) \) \( y^{\prime}=\square \)