Differentiate y=tanx/x?
3 Answers
Explanation:
#"differentiate using the "color(blue)"quotient rule"#
#"given "y=(g(x))/(h(x))" then"#
#dy/dx=(h(x)g'(x)-g(x)h'(x))/(h(x))^2#
#g(x)=tanxrArrg'(x)=sec^2x#
#h(x)=xrArrh(x)=1#
#dy/dx=(xsec^2x-tanx)/x^2#
Explanation:
You may use the quotient rule, which states that
In you case,
In order to compute
So, we have:
#f(x) = tan(x)# #f'(x) = 1/cos^2(x)# #g(x) = x# #g'(x) = 1# #g^2(x) = x^2#
Plug these values into the quotient rule I wrote at the beginning to get
You may rewrite it as
Explanation:
Using Quotient rule:
Let ,
So,