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

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

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

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

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derivative of

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x^{2} + 2 x - 18

x (lo g_{10} (∣ x ∣) - 1)

y = \frac{2 sin ( x )}{5}

x^{\frac{- 1}{2}}

\frac{x ^{3} + 1}{x ^{2}}

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