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Find the derivative $\frac{d}{dx}\left(2\ln\left(\frac{4}{x}\right)+e^{3x^2}+4\left(\frac{x^2-1}{x^2+2}\right)\right)$ using the sum rule

Used Formulas

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Solution

Formulas

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Basic Derivatives

· Derivative of a Constant
$\frac{d}{dx}\left(c\right)=0$
· Sum Rule for Differentiation
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}f\left(x\right) + \frac{d}{dx}g\left(x\right)$
$\frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right)$
· Power rule for derivatives
$\frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}$
· Quotient Rule in Differentiation
$\frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}$

Function Plot

Plotting: $\frac{-2}{x}+6e^{3x^2}x+\frac{4\left(2x\left(x^2+2\right)+2\left(-x^2+1\right)x\right)}{\left(x^2+2\right)^2}$

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sin
cos
tan
cot
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csc

asin
acos
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acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Used Formulas

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