What is the derivative of log_{5}(x^4) ?

The derivative of log_{5}(x^4) is 4/(ln(5)x)

What is the first derivative of log_{5}(x^4) ?

The first derivative of log_{5}(x^4) is 4/(ln(5)x)

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derivative of

lo g_{5} (x^{4})

\frac{4}{ln ( 5 ) x}

Solution steps

\frac{d}{d x} (lo g_{5} (x^{4}))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x ^{4} )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (x^{4}))

Apply the chain rule:

\frac{1}{x ^{4}} \frac{d}{d x} (x^{4})

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4}} \cdot 4 x^{3}

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{x ^{4}} \cdot 4 x^{3} : \frac{4}{ln ( 5 ) x}

= \frac{4}{ln ( 5 ) x}

\frac{\partial}{\partial y} (x - 1)

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

x \to 4 lim (\frac{1}{x - 2})

f (x) = \frac{4}{x} a = \frac{1}{16}

cos (x y)

What is the derivative of log_{5}(x^4) ?
The derivative of log_{5}(x^4) is 4/(ln(5)x)
What is the first derivative of log_{5}(x^4) ?
The first derivative of log_{5}(x^4) is 4/(ln(5)x)