What is (\partial)/(\partial x)(log_{10}(x+1)) ?

The answer to (\partial)/(\partial x)(log_{10}(x+1)) is 1/(ln(10)(x+1))

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(\partial)/(\partial x)(log_{10}(x+1))

\frac{\partial}{\partial x} (lo g_{10} (x + 1))

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

Solution steps

\frac{\partial}{\partial x} (lo g_{10} (x + 1))

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{x + 1} \frac{\partial}{\partial x} (x + 1)

= \frac{1}{x + 1} \frac{\partial}{\partial x} (x + 1)

\frac{\partial}{\partial x} (x + 1) = 1

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

Simplify

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

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

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What is (\partial)/(\partial x)(log_{10}(x+1)) ?
The answer to (\partial)/(\partial x)(log_{10}(x+1)) is 1/(ln(10)(x+1))