What is the derivative of (ln(3x)/(7x^2)) ?

The derivative of (ln(3x)/(7x^2)) is (1-2ln(3x))/(7x^3)

What is the first derivative of (ln(3x)/(7x^2)) ?

The first derivative of (ln(3x)/(7x^2)) is (1-2ln(3x))/(7x^3)

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\frac{d}{d x} (\frac{ln ( 3 x )}{7 x ^{2}})

\frac{1 - 2 ln ( 3 x )}{7 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{ln ( 3 x )}{7 x ^{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{7} \frac{d}{d x} (\frac{ln ( 3 x )}{x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( ln ( 3 x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ln ( 3 x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

\frac{d}{d x} (x^{2}) = 2 x

= \frac{1}{7} \cdot \frac{\frac{1}{x} x ^{2} - 2 x ln ( 3 x )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{7} \cdot \frac{\frac{1}{x} x ^{2} - 2 x ln ( 3 x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( 3 x )}{7 x ^{3}}

= \frac{1 - 2 ln ( 3 x )}{7 x ^{3}}

f (x) = \frac{1}{x}

x \to - 8 lim (\frac{x - 8}{∣ x + 8 ∣})

\int \frac{1}{x ( ln ( x ) ) ^{π}} d x

n = 0 \sum \infty (- 1)^{n} 2^{n}

\int \frac{1}{t ^{2} 121 - t ^{2}} d t

What is the derivative of (ln(3x)/(7x^2)) ?
The derivative of (ln(3x)/(7x^2)) is (1-2ln(3x))/(7x^3)
What is the first derivative of (ln(3x)/(7x^2)) ?
The first derivative of (ln(3x)/(7x^2)) is (1-2ln(3x))/(7x^3)