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Popular >

d/(ds)(s/(s^2+w^2))

Solution

\frac{d}{d s} (\frac{s}{s ^{2} + w ^{2}})

Solution

\frac{w ^{2} - s ^{2}}{( s ^{2} + w ^{2} ) ^{2}}

Solution steps

\frac{d}{d s} (\frac{s}{s ^{2} + w ^{2}})

Treat

w

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{d s}{d s} ( s ^{2} + w ^{2} ) - \frac{d}{d s} ( s ^{2} + w ^{2} ) s}{( s ^{2} + w ^{2} ) ^{2}}

\frac{d s}{d s} = 1

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

= \frac{1 \cdot ( s ^{2} + w ^{2} ) - 2 ss}{( s ^{2} + w ^{2} ) ^{2}}

1 \cdot (s^{2} + w^{2}) - 2 ss = w^{2} - s^{2}

= \frac{w ^{2} - s ^{2}}{( s ^{2} + w ^{2} ) ^{2}}

Popular Examples

derivative of-8e^{-3x}

\frac{d}{d x} (- 8 e^{- 3 x})

derivative of-18cos(3x)

\frac{d}{d x} (- 18 cos (3 x))

integral of (sin^5(θ))/(sqrt(cos(θ)))

\int \frac{sin ^{5} ( θ )}{cos ( θ )} d θ

derivative of f(x)=(3x^3+3x)(x-3)(x+5)derivative of

f (x) = (3 x^{3} + 3 x) (x - 3) (x + 5)

derivative of e^xx^4+8e^xx^3+12e^xx^2 derivative of

e^{x} x^{4} + 8 e^{x} x^{3} + 12 e^{x} x^{2}

Frequently Asked Questions (FAQ)

What is the d/(ds)(s/(s^2+w^2)) ?
The d/(ds)(s/(s^2+w^2)) is (w^2-s^2)/((s^2+w^2)^2)
What is the first d/(ds)(s/(s^2+w^2)) ?
The first d/(ds)(s/(s^2+w^2)) is (w^2-s^2)/((s^2+w^2)^2)