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Find the derivative of $\ln\left(\frac{\left(x+2\right)^5}{\sqrt[6]{3x-5}}\right)$

Step-by-step Solution

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Solution

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Final Answer

$\frac{5}{x+2}+\frac{-1}{2\left(3x-5\right)}$
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Step-by-step Solution

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Simplify the derivative by applying the properties of logarithms

$\frac{d}{dx}\left(5\ln\left(x+2\right)-\frac{1}{6}\ln\left(3x-5\right)\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{dx}\left(5\ln\left(x+2\right)-\frac{1}{6}\ln\left(3x-5\right)\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of ln(((x+2)^5)/((3x-5)^1/6)). Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant (5) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-\frac{1}{6}) is equal to the constant times the derivative of the function.

Final Answer

$\frac{5}{x+2}+\frac{-1}{2\left(3x-5\right)}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of ln(((x+2)^5)/((3x-5)^0.1667)) using the product ruleFind derivative of ln(((x+2)^5)/((3x-5)^0.1667)) using the quotient ruleFind derivative of ln(((x+2)^5)/((3x-5)^0.1667)) using logarithmic differentiationFind derivative of ln(((x+2)^5)/((3x-5)^0.1667)) using the definition

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Function Plot

Plotting: $\frac{5}{x+2}+\frac{-1}{2\left(3x-5\right)}$

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0
a
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n
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x
y
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.
(◻)
+
-
×
◻/◻
/
÷
◻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

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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.

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