What is the derivative of (1-e^{7x}/(1+e^{7x)}) ?

The derivative of (1-e^{7x}/(1+e^{7x)}) is -(14e^{7x})/((1+e^{7x))^2}

What is the first derivative of (1-e^{7x}/(1+e^{7x)}) ?

The first derivative of (1-e^{7x}/(1+e^{7x)}) is -(14e^{7x})/((1+e^{7x))^2}

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\frac{d}{d x} (\frac{1 - e ^{7 x}}{1 + e ^{7 x}})

- \frac{14 e ^{7 x}}{( 1 + e ^{7 x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - e ^{7 x}}{1 + e ^{7 x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - e ^{7 x} ) ( 1 + e ^{7 x} ) - \frac{d}{d x} ( 1 + e ^{7 x} ) ( 1 - e ^{7 x} )}{( 1 + e ^{7 x} ) ^{2}}

\frac{d}{d x} (1 - e^{7 x}) = - 7 e^{7 x}

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

= \frac{( - 7 e ^{7 x} ) ( 1 + e ^{7 x} ) - 7 e ^{7 x} ( 1 - e ^{7 x} )}{( 1 + e ^{7 x} ) ^{2}}

Simplify

\frac{( - 7 e ^{7 x} ) ( 1 + e ^{7 x} ) - 7 e ^{7 x} ( 1 - e ^{7 x} )}{( 1 + e ^{7 x} ) ^{2}} : - \frac{14 e ^{7 x}}{( 1 + e ^{7 x} ) ^{2}}

= - \frac{14 e ^{7 x}}{( 1 + e ^{7 x} ) ^{2}}

y = x^{\frac{8}{5}}

x \to 1 lim (e^{5 x^{5} - 5 x})

\int_{0}^{π} 1 - cos (2 x) d x

\int 2 x + 3 d x

\frac{d}{d x} (e^{s i n (x)} cos (sin (x)))

What is the derivative of (1-e^{7x}/(1+e^{7x)}) ?
The derivative of (1-e^{7x}/(1+e^{7x)}) is -(14e^{7x})/((1+e^{7x))^2}
What is the first derivative of (1-e^{7x}/(1+e^{7x)}) ?
The first derivative of (1-e^{7x}/(1+e^{7x)}) is -(14e^{7x})/((1+e^{7x))^2}