What is the derivative of log_{10}(1+y) ?

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

What is the first derivative of log_{10}(1+y) ?

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

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derivative of

lo g_{10} (1 + y)

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

Solution steps

\frac{d}{d y} (lo g_{10} (1 + y))

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{1 + y} \frac{d}{d y} (1 + y)

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

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

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

Simplify

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

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

y = \frac{( x ^{2} + 1 )}{x ^{3}}

t^{2} + 1

t^{2} + 2

x^{3} - 3^{x}

f (x) = - x + 2

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