What is the derivative of log_{10}(x+5) ?

The derivative of log_{10}(x+5) is 1/(ln(10)(x+5))

What is the first derivative of log_{10}(x+5) ?

The first derivative of log_{10}(x+5) is 1/(ln(10)(x+5))

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derivative of

lo g_{10} (x + 5)

\frac{1}{ln ( 10 ) ( x + 5 )}

Solution steps

\frac{d}{d x} (lo g_{10} (x + 5))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x + 5 )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (x + 5))

Apply the chain rule:

\frac{1}{x + 5} \frac{d}{d x} (x + 5)

= \frac{1}{x + 5} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= \frac{1}{ln ( 10 )} \cdot \frac{1}{x + 5} \cdot 1

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{x + 5} \cdot 1 : \frac{1}{ln ( 10 ) ( x + 5 )}

= \frac{1}{ln ( 10 ) ( x + 5 )}

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

\frac{d}{d x} (sin (2 x) sin (x))

\frac{d y}{d x}, 25 x = y^{4}

\frac{d}{d x} ((9 x^{6} + 4 x^{3})^{4})

6 x^{2}, x^{2} + 9

What is the derivative of log_{10}(x+5) ?
The derivative of log_{10}(x+5) is 1/(ln(10)(x+5))
What is the first derivative of log_{10}(x+5) ?
The first derivative of log_{10}(x+5) is 1/(ln(10)(x+5))