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

The derivative of log_{10}(x^2+x) is (2x+1)/(ln(10)(x^2+x))

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

The first derivative of log_{10}(x^2+x) is (2x+1)/(ln(10)(x^2+x))

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derivative of

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of log_{10}(x^2+x) ?
The derivative of log_{10}(x^2+x) is (2x+1)/(ln(10)(x^2+x))
What is the first derivative of log_{10}(x^2+x) ?
The first derivative of log_{10}(x^2+x) is (2x+1)/(ln(10)(x^2+x))