What is the derivative of #5x arcsin(x)#?

1 Answer
Jim G.
Oct 12, 2017

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

Explanation:

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

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

#dy/dx=g(x)h'(x)+h(x)g'(x)larr" product rule"#

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

#h(x)=arcsinxrArrh'(x)=1/sqrt(1-x^2)#

#rArrd/dx(5xarcsinx)#

#=5x xx1/sqrt(1-x^2)+arcsinx xx5#

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

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