differentiate y=5 tan^x with respect to x

Question

differentiation,y=5 tan°x

Answer 1

I read this as "Differentiate y=5tan^2(x) with respect to x."

If p=tan(x) then dp/dx=sec^2(x) and y=5p^2, dy/dp=10p.

dy/dx=dy/dp * dp/dx=10p*sec^2(x)=10tan(x)sec^2(x) by the chain rule.

This can also be written: 10tan(x)(1+tan^2(x)).

Answer 2

y = 5tan^2x

dy/dx = 5*2 tanx*d/dxtanx) =

10 tanx*sec^2(x)

 

the derivate of tanx is sec^2x