# Step-by-step Solution

## Find the derivative $\frac{d}{dx}\left(xe^{\left(3x-5\right)}+\ln\left(x-4\right)\right)$ using the sum rule

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

$\frac{1}{x-4}+e^{\left(3x-5\right)}\left(1+3x\right)$

## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(x e^{\left(3x-5\right)}+\ln\left(x-4\right)\right)$
1

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(xe^{\left(3x-5\right)}\right)+\frac{d}{dx}\left(\ln\left(x-4\right)\right)$
2

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=e^{\left(3x-5\right)}$

$e^{\left(3x-5\right)}\cdot\frac{d}{dx}\left(x\right)+x\frac{d}{dx}\left(e^{\left(3x-5\right)}\right)+\frac{d}{dx}\left(\ln\left(x-4\right)\right)$

$\frac{1}{x-4}+e^{\left(3x-5\right)}\left(1+3x\right)$
$\frac{d}{dx}\left(x e^{\left(3x-5\right)}+\ln\left(x-4\right)\right)$

Equations

~ 0.74 seconds