How do you find the derivative of #arccose^x#?

1 Answer
Feb 18, 2017

#-e^x/(sqrt(1-e^(2x)))#

Explanation:

Use the #color(blue)"standard derivative result"#

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

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(arccos(f(x)))=-1/(sqrt(1-(f(x))^2)).f'(x))color(white)(2/2)|)))#

#rArrd/dx(arccose^x)#

#=-1/(sqrt(1-(e^x)^2))xxd/dx(e^x)#

#=-e^x/(sqrt(1-e^(2x))#