How do you find the derivative of #f(x)=3((arcsinx)^2)#?

1 Answer
Apr 28, 2018

#f'(x)=(6arcsinx)/(sqrt(1-x^2))#

Explanation:

#•color(white)(x)d/dx(arcsinx)=1/(sqrt(1-x^2))#

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

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

#f'(x)=g'(h(x))xxh'(x)#

#rArrf'(x)=3[2arcsinx xxd/dx(arcsinx)]#

#color(white)(rArrf'(x))=3(2arcsinx xx1/(sqrt(1-x^2)))#

#color(white)(rArrf'(x))=(6arcsinx)/(sqrt(1-x^2))#