Step-by-step explanation:
so
[tex]f(x)=9x^1^0tan^-^1(x)[/tex]
to find [tex]f'(x)=[/tex]
[tex]d/dx(9x^1^0tan^-^1(x))[/tex]
differentiation is linear so we solve differentiate separately and pull out constant factors
[tex][a.u(x)+b.v(x)]'=a.u'(x)+b.v'(x)[/tex]
[tex]=9.d/dx(x^1^0tan^-^1(x))[/tex]
applying product rule
[tex][u(x).v(x)]'=u'(x).v(x)+u(x).v'(x)[/tex]
[tex]=9(d/dx[x^1^0].tan(x)+x^1^0.d/dx[tan(x)])[/tex]
[tex]=9(10x^9tan(x)+x^1^0.(1/x^2+1))[/tex]
[tex]=9(10x^9tan(x)+x^1^0/x^2+1)[/tex]
simplify
[tex]f'(x)=90x^9tan(x)+(9x^1^0/x^2+1)[/tex]
