How do you find the derivative of #5x arcsin(x)#?

1 Answer
Jim G.
Mar 3, 2017

#(5x)/(sqrt(1-x^2))+5arcsin(x)#

Explanation:

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(arcsinx)=1/(sqrt(1-x^2)))color(white)(2/2)|)))#

#"let "f(x)=5xarcsin(x)#

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

#"Given "f(x)=g(x).h(x)" then"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(f'(x)=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))#

#"here "g(x)=5xrArrg'(x)=5#

#"and "h(x)=arcsin(x)rArrh'(x)=1/(sqrt(1-x^2))#

#rArrf'(x)=5x. 1/(sqrt(1-x^2))+5arcsin(x)#

#rArrf'(x)=(5x)/(sqrt(1-x^2))+5arcsin(x)#

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