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

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

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

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

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

\frac{3}{ln ( 10 ) x}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{3}{ln ( 10 ) x}

y = x^{3} - 15 x, (2, - 22)

9 + 5 x^{2} - 2 x^{3}

\int \frac{x ^{2} - 1}{x ^{4}} d x

16 y^{^{''}} + 7 y = 0

\frac{d}{d x} (1 - e^{x} + (e - 1) sin ((\frac{π}{2}) x))

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