How do you find the derivative of y=1+tan^2(5x)?

1 Answer
May 31, 2017

y'=10sin(5x)/cos^3(5x)

Explanation:

Since the derivative of a constant function is null,

and the derivative of tan(color(blue)f(x)) is

1/cos^2color(blue)(f(x))*f'(x)

and the derivative of (color(red)(g(x)^2)) is color(red)(2g(x))*g'(x),

then

y'=0+color(red)(2tan(5x))*1/cos^2(color(blue)(5x))*5

=10sin(5x)/cos(5x)*1/cos^2(5x)

=10sin(5x)/cos^3(5x)