Question

Find the derivative of y=5^(1-4x)
lny=(1-4x)ln5

Can I split it?
lny=ln5-4xln5
1/y dy/dx = -[4ln5/(4xln5)^2]
dy/dx=-[4ln5/(4xln5)^2]y

Thanks.

Answer 1

Can I split it?
lny=ln5-4xln5

Yes, that is valid.

ln y = ln 5 - (4 ln 5) x

since [4 ln 5 is a constant]

(1/y) dy/dx = 0 - (4 ln 5) dx/dx

Answer 2

Thank you!