What is the derivative of (ln(x)(ln(3x-7))) ?

The derivative of (ln(x)(ln(3x-7))) is (ln(3x-7))/x+(3ln(x))/(3x-7)

What is the first derivative of (ln(x)(ln(3x-7))) ?

The first derivative of (ln(x)(ln(3x-7))) is (ln(3x-7))/x+(3ln(x))/(3x-7)

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\frac{d}{d x} ((ln (x)) (ln (3 x - 7)))

\frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

Solution steps

\frac{d}{d x} ((ln (x)) (ln (3 x - 7)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = ln (3 x - 7)

= \frac{d}{d x} (ln (x)) ln (3 x - 7) + \frac{d}{d x} (ln (3 x - 7)) ln (x)

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

\frac{d}{d x} (ln (3 x - 7)) = \frac{3}{3 x - 7}

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

Simplify

\frac{1}{x} ln (3 x - 7) + \frac{3}{3 x - 7} ln (x) : \frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

= \frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

f (x) = e^{- \frac{7}{x ^{7}}}

x \to \infty lim (1 + \frac{4}{x})

\frac{\partial}{\partial x} (- 2 e^{- x^{2} + y} y x)

x, \frac{1}{3} x, 16

y^{^{'}} + \frac{y}{x} = 0

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