How do you differentiate $f (x) = x sec x$ $f(x)=xsecx$ ?

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Answer 1 · 2016-11-10T14:48:11

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

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;

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

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

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