What is the derivative of (5^x+2/(5^x+1)) ?

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

What is the first derivative of (5^x+2/(5^x+1)) ?

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

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\frac{d}{d x} (\frac{5 ^{x} + 2}{5 ^{x} + 1})

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

Solution steps

\frac{d}{d x} (\frac{5 ^{x} + 2}{5 ^{x} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 5 ^{x} + 2 ) ( 5 ^{x} + 1 ) - \frac{d}{d x} ( 5 ^{x} + 1 ) ( 5 ^{x} + 2 )}{( 5 ^{x} + 1 ) ^{2}}

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

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

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

Simplify

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

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

y = - 8 + 5 x

\int \frac{14}{1 - cos ( 2 x )} d x

\int 6 x^{2} y - 2 x d y

\frac{\partial}{\partial x} (y x^{2} + x y^{2} + y z^{2})

\int \frac{e ^{x} ( 1 + x )}{cos ^{2} ( x e ^{x} )} d x

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