How do you find the derivative of #(x^2)(sinx)(tanx)#?

1 Answer
Jim G.
Sep 9, 2017

#2xsinxtanx+x^2cosxtanx+x^2sinxsec^2x#

Explanation:

#"differentiate using the "color(blue)"product rule"#

#"the rule for differentiating the product of 3 functions is"#

#"given "y=f(x)g(x)h(x)" then"#

#dy/dx=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)#

#f(x)=x^2rArrf'(x)=2x#

#g(x)=sinxrArrg'(x)=cosx#

#h(x)=tanxrArrh'(x)=sec^2x#

#"hence derivative"#

#=2xsinxtanx+x^2cosxtanx+x^2sinxsec^2x#

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