How do you differentiate $f (x) = x^{7} csc (x)$ $f(x)=x^7csc(x)$ using the product rule?

Question

2061 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-28T07:14:28

$f'(x)= -x^6csc(x)[xcot(x)-7]$

Keep the first factor and find the derivative of the second then add that to the derivative of the first factor and keep the 2nd factor untouched

$f(x)=uv$

$f'(x)=uv'+u'v$

$f(x)= x^7csc(x)$

$f'(x)=x^7(-csc(x) cot(x))+7x^6csc(x)$

Factor out $-x^6csc(x)$

$f'(x)= -x^6csc(x)[xcot(x)-7]$

How do you differentiate f(x)=x^7csc(x)f(x)=x7csc(x) f(x)=x^7csc(x) using the product rule?