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Find the derivative of $8\ln\left(3\left(x+y\right)-27a^{3x}\right)$

Used Formulas

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Solution

Formulas

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Basic Derivatives

$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Derivative of the natural logarithm
$\frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right)$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
· Derivative of the linear function
$\frac{d}{dx}\left(x\right)=1$

Function Plot

Plotting: $\frac{8\left(6-81a^{3x}\ln\left(a\right)\right)}{3\left(x+y-9a^{3x}\right)}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

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$\frac{d}{dx}\left(\ln\left(x\right)\right)^2$

Find the derivative

$\frac{d}{dx}\left(x^2+y^2\right)$

Find the derivative

$\frac{d}{dx}\left(x-2^{4x}\right)$

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

See formulas (4)

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