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

The derivative of log_{10}((x^2+1^2)) is (4x)/(ln(10)(x^2+1))

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

The first derivative of log_{10}((x^2+1^2)) is (4x)/(ln(10)(x^2+1))

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

\frac{4 x}{ln ( 10 ) ( x ^{2} + 1 )}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} + 1)^{2}) = 4 x (x^{2} + 1)

= \frac{1}{ln ( 10 )} \cdot \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1)

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{( x ^{2} + 1 ) ^{2}} \cdot 4 x (x^{2} + 1) : \frac{4 x}{ln ( 10 ) ( x ^{2} + 1 )}

= \frac{4 x}{ln ( 10 ) ( x ^{2} + 1 )}

\int x - cos (x) d x

e^{- s} \frac{( s ^{2} + 2 )}{s ^{3}}

\int \frac{1}{y + y ^{3}} d y

\frac{\partial}{\partial x} (1 (x - y) e^{1 y + 3 x^{2}})

f (x) = \frac{64}{( 1 + 4 x ) ^{3}}

What is the derivative of log_{10}((x^2+1^2)) ?
The derivative of log_{10}((x^2+1^2)) is (4x)/(ln(10)(x^2+1))
What is the first derivative of log_{10}((x^2+1^2)) ?
The first derivative of log_{10}((x^2+1^2)) is (4x)/(ln(10)(x^2+1))