What is the derivative of (6e^ss-5e^s)/((6s+1)^2) ?

The derivative of (6e^ss-5e^s)/((6s+1)^2) is (e^s(36s^2-60s+61))/((6s+1)^3)

What is the first derivative of (6e^ss-5e^s)/((6s+1)^2) ?

The first derivative of (6e^ss-5e^s)/((6s+1)^2) is (e^s(36s^2-60s+61))/((6s+1)^3)

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derivative of

\frac{6 e ^{s} s - 5 e ^{s}}{( 6 s + 1 ) ^{2}}

\frac{e ^{s} ( 36 s ^{2} - 60 s + 61 )}{( 6 s + 1 ) ^{3}}

Solution steps

\frac{d}{d s} (\frac{6 e ^{s} s - 5 e ^{s}}{( 6 s + 1 ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d s} ( 6 e ^{s} s - 5 e ^{s} ) ( 6 s + 1 ) ^{2} - \frac{d}{d s} ( ( 6 s + 1 ) ^{2} ) ( 6 e ^{s} s - 5 e ^{s} )}{( ( 6 s + 1 ) ^{2} ) ^{2}}

\frac{d}{d s} (6 e^{s} s - 5 e^{s}) = 6 e^{s} s + e^{s}

\frac{d}{d s} ((6 s + 1)^{2}) = 12 (6 s + 1)

= \frac{( 6 e ^{s} s + e ^{s} ) ( 6 s + 1 ) ^{2} - 12 ( 6 s + 1 ) ( 6 e ^{s} s - 5 e ^{s} )}{( ( 6 s + 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 6 e ^{s} s + e ^{s} ) ( 6 s + 1 ) ^{2} - 12 ( 6 s + 1 ) ( 6 e ^{s} s - 5 e ^{s} )}{( ( 6 s + 1 ) ^{2} ) ^{2}} : \frac{e ^{s} ( 36 s ^{2} - 60 s + 61 )}{( 6 s + 1 ) ^{3}}

= \frac{e ^{s} ( 36 s ^{2} - 60 s + 61 )}{( 6 s + 1 ) ^{3}}

\int \frac{x ^{3} + 22}{x ^{2} + 7 x + 12} d x

y = 3 e^{x} + x, (0, 3)

\frac{d}{d x} (2 x^{2} - 8)

\frac{7}{( 7 - x ^{8} ) ^{\frac{3}{2}}}

(sin^{2} (x) + 1)^{5}

What is the derivative of (6e^ss-5e^s)/((6s+1)^2) ?
The derivative of (6e^ss-5e^s)/((6s+1)^2) is (e^s(36s^2-60s+61))/((6s+1)^3)
What is the first derivative of (6e^ss-5e^s)/((6s+1)^2) ?
The first derivative of (6e^ss-5e^s)/((6s+1)^2) is (e^s(36s^2-60s+61))/((6s+1)^3)