What is the derivative of log_{7}((x^4/(5x+11))) ?

The derivative of log_{7}((x^4/(5x+11))) is (15x+44)/(ln(7)x(5x+11))

What is the first derivative of log_{7}((x^4/(5x+11))) ?

The first derivative of log_{7}((x^4/(5x+11))) is (15x+44)/(ln(7)x(5x+11))

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\frac{d}{d x} (lo g_{7} (\frac{x ^{4}}{5 x + 11}))

\frac{15 x + 44}{ln ( 7 ) x ( 5 x + 11 )}

Solution steps

\frac{d}{d x} (lo g_{7} (\frac{x ^{4}}{5 x + 11}))

Apply log rule:

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

= \frac{d}{d x} \frac{ln ( \frac{x ^{4}}{5 x + 11} )}{ln ( 7 )}

Take the constant out:

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

= \frac{1}{ln ( 7 )} \frac{d}{d x} (ln (\frac{x ^{4}}{5 x + 11}))

Apply the chain rule:

\frac{1}{\frac{x ^{4}}{5 x + 11}} \frac{d}{d x} (\frac{x ^{4}}{5 x + 11})

= \frac{1}{\frac{x ^{4}}{5 x + 11}} \frac{d}{d x} (\frac{x ^{4}}{5 x + 11})

\frac{d}{d x} (\frac{x ^{4}}{5 x + 11}) = \frac{15 x ^{4} + 44 x ^{3}}{( 5 x + 11 ) ^{2}}

= \frac{1}{ln ( 7 )} \cdot \frac{1}{\frac{x ^{4}}{5 x + 11}} \cdot \frac{15 x ^{4} + 44 x ^{3}}{( 5 x + 11 ) ^{2}}

Simplify

\frac{1}{ln ( 7 )} \cdot \frac{1}{\frac{x ^{4}}{5 x + 11}} \cdot \frac{15 x ^{4} + 44 x ^{3}}{( 5 x + 11 ) ^{2}} : \frac{15 x + 44}{ln ( 7 ) x ( 5 x + 11 )}

= \frac{15 x + 44}{ln ( 7 ) x ( 5 x + 11 )}

x^{2} (1 - 4 x)

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

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

t^{3} \cdot sin (3 t)

\frac{\partial}{\partial t} (cos (2 t))

What is the derivative of log_{7}((x^4/(5x+11))) ?
The derivative of log_{7}((x^4/(5x+11))) is (15x+44)/(ln(7)x(5x+11))
What is the first derivative of log_{7}((x^4/(5x+11))) ?
The first derivative of log_{7}((x^4/(5x+11))) is (15x+44)/(ln(7)x(5x+11))