What is the derivative of ln(8x-5*7^{5x-2}) ?

The derivative of ln(8x-5*7^{5x-2}) is (8*7^{5x-2})/(8x-5)+5ln(7)*7^{5x-2}ln(8x-5)

What is the first derivative of ln(8x-5*7^{5x-2}) ?

The first derivative of ln(8x-5*7^{5x-2}) is (8*7^{5x-2})/(8x-5)+5ln(7)*7^{5x-2}ln(8x-5)

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\frac{d}{d x} (ln (8 x - 5) \cdot 7^{5 x - 2})

\frac{8 \cdot 7 ^{5 x - 2}}{8 x - 5} + 5 ln (7) \cdot 7^{5 x - 2} ln (8 x - 5)

Solution steps

\frac{d}{d x} (ln (8 x - 5) \cdot 7^{5 x - 2})

Apply the Product Rule:

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

f = ln (8 x - 5), g = 7^{5 x - 2}

= \frac{d}{d x} (ln (8 x - 5)) 7^{5 x - 2} + \frac{d}{d x} (7^{5 x - 2}) ln (8 x - 5)

\frac{d}{d x} (ln (8 x - 5)) = \frac{8}{8 x - 5}

\frac{d}{d x} (7^{5 x - 2}) = 5 ln (7) \cdot 7^{5 x - 2}

= \frac{8}{8 x - 5} \cdot 7^{5 x - 2} + 5 ln (7) \cdot 7^{5 x - 2} ln (8 x - 5)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 \cdot 7 ^{5 x - 2}}{8 x - 5} + 5 ln (7) \cdot 7^{5 x - 2} ln (8 x - 5)

What is the derivative of ln(8x-5*7^{5x-2}) ?
The derivative of ln(8x-5*7^{5x-2}) is (8*7^{5x-2})/(8x-5)+5ln(7)*7^{5x-2}ln(8x-5)
What is the first derivative of ln(8x-5*7^{5x-2}) ?
The first derivative of ln(8x-5*7^{5x-2}) is (8*7^{5x-2})/(8x-5)+5ln(7)*7^{5x-2}ln(8x-5)