How do you differentiate # y =(5x^2-x+1)^(5/2 # using the chain rule?

1 Answer
Jul 24, 2017

Answer:

#dy/dx=5/2(10x-1)(5x^2-x+1)^(3/2)#

Explanation:

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

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

#dy/dx=f'(g(x))xxg'(x)larr" chain rule"#

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

#rArrdy/dx=5/2(5x^2-x+1)^(3/2)xxd/dx(5x^2-x+1)#

#color(white)(rArrdy/dx)=5/2(10x-1)(5x^2-x+1)^(3/2)#