What is the derivative of (7e^ss-6e^s)/((7s+1)^2) ?

The derivative of (7e^ss-6e^s)/((7s+1)^2) is (e^s(49s^2-84s+85))/((7s+1)^3)

What is the first derivative of (7e^ss-6e^s)/((7s+1)^2) ?

The first derivative of (7e^ss-6e^s)/((7s+1)^2) is (e^s(49s^2-84s+85))/((7s+1)^3)

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derivative of

\frac{7 e ^{s} s - 6 e ^{s}}{( 7 s + 1 ) ^{2}}

\frac{e ^{s} ( 49 s ^{2} - 84 s + 85 )}{( 7 s + 1 ) ^{3}}

Solution steps

\frac{d}{d s} (\frac{7 e ^{s} s - 6 e ^{s}}{( 7 s + 1 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( 7 e ^{s} s - 6 e ^{s} ) ( 7 s + 1 ) ^{2} - \frac{d}{d s} ( ( 7 s + 1 ) ^{2} ) ( 7 e ^{s} s - 6 e ^{s} )}{( ( 7 s + 1 ) ^{2} ) ^{2}}

\frac{d}{d s} (7 e^{s} s - 6 e^{s}) = 7 e^{s} s + e^{s}

\frac{d}{d s} ((7 s + 1)^{2}) = 14 (7 s + 1)

= \frac{( 7 e ^{s} s + e ^{s} ) ( 7 s + 1 ) ^{2} - 14 ( 7 s + 1 ) ( 7 e ^{s} s - 6 e ^{s} )}{( ( 7 s + 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 7 e ^{s} s + e ^{s} ) ( 7 s + 1 ) ^{2} - 14 ( 7 s + 1 ) ( 7 e ^{s} s - 6 e ^{s} )}{( ( 7 s + 1 ) ^{2} ) ^{2}} : \frac{e ^{s} ( 49 s ^{2} - 84 s + 85 )}{( 7 s + 1 ) ^{3}}

= \frac{e ^{s} ( 49 s ^{2} - 84 s + 85 )}{( 7 s + 1 ) ^{3}}

x \to 81 lim (\frac{x ^{2}}{9} - \frac{9}{x})

\frac{\partial}{\partial s} (3 s t)

\frac{\partial}{\partial x} (ln (sec (x)))

n = 1 \sum \infty \frac{1}{2 ^{2 n}}

\int (4 csc^{2} (t) - 3 e^{t}) d t

What is the derivative of (7e^ss-6e^s)/((7s+1)^2) ?
The derivative of (7e^ss-6e^s)/((7s+1)^2) is (e^s(49s^2-84s+85))/((7s+1)^3)
What is the first derivative of (7e^ss-6e^s)/((7s+1)^2) ?
The first derivative of (7e^ss-6e^s)/((7s+1)^2) is (e^s(49s^2-84s+85))/((7s+1)^3)