differentiate

Question

-5^{3x^2}

Answer 1

There may be cleaner ways to do this but this does work.

 

Let y=-5^{3x^2} 

 

and e^u = 5^{3x^2} 

 

Then take ln() of both sides

 

ln(e^u)=u=3x² ln(5)

 

Find du/dx

 

du/dx=6ln(5)x

 

Make substitution 

y=-e^u 

 

dy/dx=(dy/du).(du/dx) by Chain Rule

 

dy/dx=-e^u .6ln(5)x

 

Back substitute for e^u

 

dy/dx=-6ln(5)x5^{3x^2}