Question

differentiate -5e^4x

Answer 1

The constant won't affect the differentiation process, so we can pull it out front.
\[\Large \color{royalblue}{\left(\color{black}{-5e^{4x}}\right)'}\quad=\quad\color{black}{-5}\color{royalblue}{\left(\color{black}{e^{4x}}\right)'}\]
Recall the rule for differentiating an exponential of base e:\[\Large \frac{d}{dx}e^u\quad=\quad e^u\frac{du}{dx}\quad=\quad e^u\;(u)'\]

Applying this rule gives us:\[\Large \color{black}{-5}\color{royalblue}{\left(\color{black}{e^{4x}}\right)'}\quad=\quad -5e^{4x}\color{royalblue}{\left(\color{black}{4x}\right)'}\]

Answer 2

I took the derivative of the exponential ( it gave us the same thing back).
Then we have to apply the chain rule, multiplying by the derivative of the inner function ( the contents of the exponent in this case ).

Answer 3

Derivative of 4x?