What is the derivative of log_{8}(5x^3+3x) ?

The derivative of log_{8}(5x^3+3x) is (5x^2+1)/(ln(2)x(5x^2+3))

What is the first derivative of log_{8}(5x^3+3x) ?

The first derivative of log_{8}(5x^3+3x) is (5x^2+1)/(ln(2)x(5x^2+3))

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derivative of

lo g_{8} (5 x^{3} + 3 x)

\frac{5 x ^{2} + 1}{ln ( 2 ) x ( 5 x ^{2} + 3 )}

Solution steps

\frac{d}{d x} (lo g_{8} (5 x^{3} + 3 x))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 5 x ^{3} + 3 x )}{ln ( 8 )})

Take the constant out:

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

= \frac{1}{ln ( 8 )} \frac{d}{d x} (ln (5 x^{3} + 3 x))

Apply the chain rule:

\frac{1}{5 x ^{3} + 3 x} \frac{d}{d x} (5 x^{3} + 3 x)

= \frac{1}{5 x ^{3} + 3 x} \frac{d}{d x} (5 x^{3} + 3 x)

\frac{d}{d x} (5 x^{3} + 3 x) = 15 x^{2} + 3

= \frac{1}{ln ( 8 )} \cdot \frac{1}{5 x ^{3} + 3 x} (15 x^{2} + 3)

Simplify

\frac{1}{ln ( 8 )} \cdot \frac{1}{5 x ^{3} + 3 x} (15 x^{2} + 3) : \frac{5 x ^{2} + 1}{ln ( 2 ) x ( 5 x ^{2} + 3 )}

= \frac{5 x ^{2} + 1}{ln ( 2 ) x ( 5 x ^{2} + 3 )}

What is the derivative of log_{8}(5x^3+3x) ?
The derivative of log_{8}(5x^3+3x) is (5x^2+1)/(ln(2)x(5x^2+3))
What is the first derivative of log_{8}(5x^3+3x) ?
The first derivative of log_{8}(5x^3+3x) is (5x^2+1)/(ln(2)x(5x^2+3))