What is the derivative of G(s)=(8s^2)/(7e^s+s) ?

The derivative of G(s)=(8s^2)/(7e^s+s) is (8(s^2-7e^ss^2+14e^ss))/((7e^s+s)^2)

What is the first derivative of G(s)=(8s^2)/(7e^s+s) ?

The first derivative of G(s)=(8s^2)/(7e^s+s) is (8(s^2-7e^ss^2+14e^ss))/((7e^s+s)^2)

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derivative of

G (s) = \frac{8 s ^{2}}{7 e ^{s} + s}

\frac{8 ( s ^{2} - 7 e ^{s} s ^{2} + 14 e ^{s} s )}{( 7 e ^{s} + s ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{8 s ^{2}}{7 e ^{s} + s})

Take the constant out:

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

= 8 \frac{d}{d s} (\frac{s ^{2}}{7 e ^{s} + s})

Apply the Quotient Rule:

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

= 8 \cdot \frac{\frac{d}{d s} ( s ^{2} ) ( 7 e ^{s} + s ) - \frac{d}{d s} ( 7 e ^{s} + s ) s ^{2}}{( 7 e ^{s} + s ) ^{2}}

\frac{d}{d s} (s^{2}) = 2 s

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

= 8 \cdot \frac{2 s ( 7 e ^{s} + s ) - ( 7 e ^{s} + 1 ) s ^{2}}{( 7 e ^{s} + s ) ^{2}}

Simplify

8 \cdot \frac{2 s ( 7 e ^{s} + s ) - ( 7 e ^{s} + 1 ) s ^{2}}{( 7 e ^{s} + s ) ^{2}} : \frac{8 ( s ^{2} - 7 e ^{s} s ^{2} + 14 e ^{s} s )}{( 7 e ^{s} + s ) ^{2}}

= \frac{8 ( s ^{2} - 7 e ^{s} s ^{2} + 14 e ^{s} s )}{( 7 e ^{s} + s ) ^{2}}

\frac{( x ^{3} - 6 x ) ^{9}}{9}

\int \frac{( x ^{3} )}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (2 x^{3} y + 4)

x \to 3 + lim (\frac{1}{x - 3})

\int_{- \infty}^{0} \frac{1}{5 - 3 x} d x

What is the derivative of G(s)=(8s^2)/(7e^s+s) ?
The derivative of G(s)=(8s^2)/(7e^s+s) is (8(s^2-7e^ss^2+14e^ss))/((7e^s+s)^2)
What is the first derivative of G(s)=(8s^2)/(7e^s+s) ?
The first derivative of G(s)=(8s^2)/(7e^s+s) is (8(s^2-7e^ss^2+14e^ss))/((7e^s+s)^2)