What is the derivative of (6^x+5/(6^x+2)) ?

The derivative of (6^x+5/(6^x+2)) is (ln(6)*3^x*2^{x+1}-5ln(6)*6^x)/((6^x+2)^2)

What is the first derivative of (6^x+5/(6^x+2)) ?

The first derivative of (6^x+5/(6^x+2)) is (ln(6)*3^x*2^{x+1}-5ln(6)*6^x)/((6^x+2)^2)

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\frac{d}{d x} (\frac{6 ^{x} + 5}{6 ^{x} + 2})

\frac{ln ( 6 ) \cdot 3 ^{x} \cdot 2 ^{x + 1} - 5 ln ( 6 ) \cdot 6 ^{x}}{( 6 ^{x} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{6 ^{x} + 5}{6 ^{x} + 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 6 ^{x} + 5 ) ( 6 ^{x} + 2 ) - \frac{d}{d x} ( 6 ^{x} + 2 ) ( 6 ^{x} + 5 )}{( 6 ^{x} + 2 ) ^{2}}

\frac{d}{d x} (6^{x} + 5) = ln (6) \cdot 6^{x}

\frac{d}{d x} (6^{x} + 2) = ln (6) \cdot 6^{x}

= \frac{ln ( 6 ) \cdot 6 ^{x} ( 6 ^{x} + 2 ) - ln ( 6 ) \cdot 6 ^{x} ( 6 ^{x} + 5 )}{( 6 ^{x} + 2 ) ^{2}}

Expand

ln (6) \cdot 6^{x} (6^{x} + 2) - ln (6) \cdot 6^{x} (6^{x} + 5) : ln (6) \cdot 3^{x} \cdot 2^{x + 1} - 5 ln (6) \cdot 6^{x}

= \frac{ln ( 6 ) \cdot 3 ^{x} \cdot 2 ^{x + 1} - 5 ln ( 6 ) \cdot 6 ^{x}}{( 6 ^{x} + 2 ) ^{2}}

\int sin (y) sin (x) d y

\int e^{l n (x + 2)} d x

y^{^{''}} + 1.9 \cdot y^{^{'}} = 0, y (0) = 0, y^{^{'}} (0) = 1

\int \frac{x}{x ^{2} + x - 1} d x

\frac{d}{d x} (sec (8 x^{3} + 1))

What is the derivative of (6^x+5/(6^x+2)) ?
The derivative of (6^x+5/(6^x+2)) is (ln(6)*3^x*2^{x+1}-5ln(6)*6^x)/((6^x+2)^2)
What is the first derivative of (6^x+5/(6^x+2)) ?
The first derivative of (6^x+5/(6^x+2)) is (ln(6)*3^x*2^{x+1}-5ln(6)*6^x)/((6^x+2)^2)