What is the derivative of log_{10}((3x+2)^3) ?

The derivative of log_{10}((3x+2)^3) is 9/(ln(10)(3x+2))

What is the first derivative of log_{10}((3x+2)^3) ?

The first derivative of log_{10}((3x+2)^3) is 9/(ln(10)(3x+2))

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derivative of

lo g_{10} ((3 x + 2)^{3})

\frac{9}{ln ( 10 ) ( 3 x + 2 )}

Solution steps

\frac{d}{d x} (lo g_{10} ((3 x + 2)^{3}))

Apply log rule:

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

= \frac{d}{d x} \frac{ln ( ( 3 x + 2 ) ^{3} )}{ln ( 10 )}

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln ((3 x + 2)^{3}))

Apply the chain rule:

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

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

\frac{d}{d x} ((3 x + 2)^{3}) = 9 (3 x + 2)^{2}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{( 3 x + 2 ) ^{3}} \cdot 9 (3 x + 2)^{2}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{( 3 x + 2 ) ^{3}} \cdot 9 (3 x + 2)^{2} : \frac{9}{ln ( 10 ) ( 3 x + 2 )}

= \frac{9}{ln ( 10 ) ( 3 x + 2 )}

cos^{2} (\frac{x}{2})

\frac{d}{d t} (\frac{1}{2 \cdot a \cdot t ^{2}})

y = \frac{1}{x ^{2} + x ^{2}}

\frac{2}{x + 10 x + 5}

y = (x^{2} + 3 x)^{4}

What is the derivative of log_{10}((3x+2)^3) ?
The derivative of log_{10}((3x+2)^3) is 9/(ln(10)(3x+2))
What is the first derivative of log_{10}((3x+2)^3) ?
The first derivative of log_{10}((3x+2)^3) is 9/(ln(10)(3x+2))