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

The derivative of y=log_{5}(sqrt(5x+4)) is 5/(2ln(5)(5x+4))

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

The first derivative of y=log_{5}(sqrt(5x+4)) is 5/(2ln(5)(5x+4))

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derivative of

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

\frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{5 x + 4} \frac{d}{d x} (5 x + 4)

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

\frac{d}{d x} (5 x + 4) = \frac{5}{2 5 x + 4}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{5 x + 4} \cdot \frac{5}{2 5 x + 4}

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{5 x + 4} \cdot \frac{5}{2 5 x + 4} : \frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

= \frac{5}{2 ln ( 5 ) ( 5 x + 4 )}

\frac{\partial}{\partial y} (4 - x^{2} - 4 y^{2})

n = 0 \sum \infty 1 0^{n} x^{n}

\int x^{2} e^{10 x} d x

y = \frac{1 + x f ( x )}{x}

\frac{\partial}{\partial x} ((x - y)^{4})

What is the derivative of y=log_{5}(sqrt(5x+4)) ?
The derivative of y=log_{5}(sqrt(5x+4)) is 5/(2ln(5)(5x+4))
What is the first derivative of y=log_{5}(sqrt(5x+4)) ?
The first derivative of y=log_{5}(sqrt(5x+4)) is 5/(2ln(5)(5x+4))