What is the derivative of log_{5}(sqrt(7x+3)) ?

The derivative of log_{5}(sqrt(7x+3)) is 7/(2ln(5)(7x+3))

What is the first derivative of log_{5}(sqrt(7x+3)) ?

The first derivative of log_{5}(sqrt(7x+3)) is 7/(2ln(5)(7x+3))

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derivative of

lo g_{5} (7 x + 3)

\frac{7}{2 ln ( 5 ) ( 7 x + 3 )}

Solution steps

\frac{d}{d x} (lo g_{5} (7 x + 3))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( 7 x + 3 )}{ln ( 5 )})

Take the constant out:

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

= \frac{1}{ln ( 5 )} \frac{d}{d x} (ln (7 x + 3))

Apply the chain rule:

\frac{1}{7 x + 3} \frac{d}{d x} (7 x + 3)

= \frac{1}{7 x + 3} \frac{d}{d x} (7 x + 3)

\frac{d}{d x} (7 x + 3) = \frac{7}{2 7 x + 3}

= \frac{1}{ln ( 5 )} \cdot \frac{1}{7 x + 3} \cdot \frac{7}{2 7 x + 3}

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{7 x + 3} \cdot \frac{7}{2 7 x + 3} : \frac{7}{2 ln ( 5 ) ( 7 x + 3 )}

= \frac{7}{2 ln ( 5 ) ( 7 x + 3 )}

\int x (3 + 4 x)^{4} d x

\frac{x ^{4} + 1}{y} \frac{d y}{d x} = - \frac{x ^{3}}{4}

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

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\int_{0}^{2 π} 20 + 16 t^{2} d t

What is the derivative of log_{5}(sqrt(7x+3)) ?
The derivative of log_{5}(sqrt(7x+3)) is 7/(2ln(5)(7x+3))
What is the first derivative of log_{5}(sqrt(7x+3)) ?
The first derivative of log_{5}(sqrt(7x+3)) is 7/(2ln(5)(7x+3))