Question

How do you differentiate `f(x)=xsecx`?

Answer 1

`f'(x) = (1+xtanx)secx`

Explanation:

If you are studying maths, then you should learn the Product Rule for Differentiation, and practice how to use it:

`d/dx(uv)=u(dv)/dx+(du)/dxv`, or, `(uv)' = (du)v + u(dv)`

I was taught to remember the rule in words; "The first times the derivative of the second plus the derivative of the first times the second ".

So with `f(x)=xsecx` we have;

`{ ("Let "u=x, => , (du)/dx=1), ("And "v=secx, =>, (dv)/dx=secxtanx ) :}`

`d/dx(uv)=u(dv)/dx + (du)/dxv`
`:. d/dx(xsecx)=(x)(secxtanx) + (1)(secx)`
`:. f'(x) = xsecxtanx + secx`
`:. f'(x) = (1+xtanx)secx`