How do you find the derivative of #6(z^2+z-1)^-1#?
2 Answers
Aug 30, 2017
Explanation:
#"differentiate using the "color(blue)"chain rule"#
#"given "y=f(g(x)" then"#
#dy/dx=f'(g(x))xxg'(x)larr" chain rule"#
#d/dz(6(z^2+z-1)^-1)#
#=-6(z^2+z-1)^-2xxd/dz(z^2+z-1)#
#=(-6(2z+1))/(z^2+z-1)^2=-(12z+6)/(z^2+z-1)^2#
Aug 30, 2017
Recall the power rule:
Combining the chain rule with the power rule for some function
Thus:
#d/(dz)6(z^2+z-1)^-1=6(-1(z^2+z-1)^-2)d/(dz)(z^2+z-1)#
And we can use the power rule to find the derivative of
#d/(dz)6(z^2+z-1)^-1=-6(z^2+z-1)^-2(2z+1)#
#=color(blue)((-6(2z+1))/(z^2+z-1)^2#