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

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

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

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

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derivative of

lo g_{10} ((x + 1)^{2})

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

Solution steps

\frac{d}{d x} (lo g_{10} ((x + 1)^{2}))

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{( x + 3 )}{2}

(e^{- 3} t)^{^{'}}

sin^{2} (x^{2}) - cos^{2} (x^{2})

(3 x)^{\frac{1}{2}}

y = ln (x) sec^{3} (x)

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