how do you find the derivative of (5/4)e^(4x)

Question

zepdrix · Answer

Constant coefficients will not affect the differentiation process at all. So let's pull the 5/4's outside of the derivative operation, like so,

$$\large \frac{d}{dx}\left(\frac{5}{4}e^{4x}\right) \qquad = \qquad \frac{5}{4}\cdot \frac{d}{dx}\left(e^{4x}\right)$$


From here, do you remember the derivative of $\large e^x$?

anonymous · Answer

isnt is just e^x

zepdrix · Answer

Yes correct. The derivative gives us back `the same thing we started with`.
That will happen here as well, except, since our exponent contains `more than just X`, we'll have to apply the chain rule.

zepdrix · Answer

$$\large \frac{5}{4}\cdot \frac{d}{dx}\left(e^{4x}\right) \qquad = \qquad \frac{5}{4}\left(e^{4x}\right)\color{royalblue}{\frac{d}{dx}\left(4x\right)}$$

Taking the derivative gave us e^4x again.
But we have to apply the chain rule ~ Multiply by the derivative of the exponent.
So we still need to differentiate this blue part.

anonymous · Answer

the derivative of the blue part is just 4

zepdrix · Answer

sounds good! c: So just simplify things down from there.

anonymous · Answer

So I would get 5e^4x ?

zepdrix · Answer

yes

anonymous · Answer

Thanks :)

zepdrix · Answer

np