Answer:
[tex]f'(x)=2x \sec^2(x^2+5)[/tex]
Step-by-step explanation:
To differentiate this we will need to use the chain rule:
[tex][h(g(x))]'=g'(x) \cdot h'(g(x))[/tex].
We will also have to keep in mind how to differentiate the following:
[tex]\tan(\theta)[/tex] with repect to [tex]\theta[/tex]
[tex]x^2+5[/tex] with respect to [tex]x[/tex].
[tex]f(x)=\tan(x^2+5)[/tex]
Derivative of both sides:
[tex]f'(x)=(x^2+5)'\cdot (\tan)'(x^2+5)[/tex]
[tex]f'(x)=(2x+0) \cdot \sec^2(x^2+5)[/tex]
[tex]f'(x)=2x \sec^2(x^2+5)[/tex]
