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

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

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

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

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derivative of

y = lo g_{5} (x) + lo g_{5} (x^{4})

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

Solution steps

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

Simplify

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

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{x ^{5}} \frac{d}{d x} (x^{5})

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

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

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

Simplify

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

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

n = 1 \sum \infty e^{- n} n^{3}

(2 x y^{2} - 4) d x + (2 x^{2} y + 7) d y = 0

(7) (0.1)

\int_{\frac{π}{4}}^{\frac{π}{2}} cos (x) d x

\frac{\partial}{\partial x} (- \frac{9 y}{x ^{2} + y ^{2} + 7})

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