What is the derivative of 5log_{10}(4x^2) ?

The derivative of 5log_{10}(4x^2) is (10)/(ln(10)x)

What is the first derivative of 5log_{10}(4x^2) ?

The first derivative of 5log_{10}(4x^2) is (10)/(ln(10)x)

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\frac{d}{d x} (5 lo g_{10} (4 x^{2}))

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

Solution steps

\frac{d}{d x} (5 lo g_{10} (4 x^{2}))

Take the constant out:

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

= 5 \frac{d}{d x} (lo g_{10} (4 x^{2}))

Apply log rule:

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

= 5 \frac{d}{d x} (\frac{ln ( 4 x ^{2} )}{ln ( 10 )})

Take the constant out:

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

= 5 \cdot \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (4 x^{2}))

Apply the chain rule:

\frac{1}{4 x ^{2}} \frac{d}{d x} (4 x^{2})

= \frac{1}{4 x ^{2}} \frac{d}{d x} (4 x^{2})

\frac{d}{d x} (4 x^{2}) = 8 x

= 5 \cdot \frac{1}{ln ( 10 )} \cdot \frac{1}{4 x ^{2}} \cdot 8 x

Simplify

5 \cdot \frac{1}{ln ( 10 )} \cdot \frac{1}{4 x ^{2}} \cdot 8 x : \frac{10}{ln ( 10 ) x}

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

What is the derivative of 5log_{10}(4x^2) ?
The derivative of 5log_{10}(4x^2) is (10)/(ln(10)x)
What is the first derivative of 5log_{10}(4x^2) ?
The first derivative of 5log_{10}(4x^2) is (10)/(ln(10)x)