Question

If f(x) = 9x10 tan-1x, find f '(x).

Answer 1

f(x) = 9x10tan-1(x) Use the product rule to derive. Let g(x) = 9x10Let h(x) = tan-1(x) Product rule: f'(x) = g'(x)h(x) + g(x)h'(x) f'(x) = 90x9tan-1 - [9x10 / (1 + x2)]

Answer 2

Explanation:

so

`f(x)=9x^1^0tan^-^1(x)`

to find
`f'(x)=`

`d/dx(9x^1^0tan^-^1(x))`

differentiation is linear so we solve differentiate separately and pull out constant factors

`[a.u(x)+b.v(x)]'=a.u'(x)+b.v'(x)`

`=9.d/dx(x^1^0tan^-^1(x))`

applying product rule

`[u(x).v(x)]'=u'(x).v(x)+u(x).v'(x)`

`=9(d/dx[x^1^0].tan(x)+x^1^0.d/dx[tan(x)])`

`=9(10x^9tan(x)+x^1^0.(1/x^2+1))`

`=9(10x^9tan(x)+x^1^0/x^2+1)`

simplify

`f'(x)=90x^9tan(x)+(9x^1^0/x^2+1)`