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Popular >

d/(ds)(sL({y}(s)))

Solution

\frac{d}{d s} (s L (y (s)))

Solution

L (y (s) + s \frac{d}{d s} (y (s)))

Solution steps

\frac{d}{d s} (s L (y (s)))

Take the constant out:

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

= L \frac{d}{d s} (s y (s))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = s, g = y (s)

= L (\frac{d s}{d s} y (s) + \frac{d}{d s} (y (s)) s)

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

= L (1 \cdot y (s) + \frac{d}{d s} (y (s)) s)

Simplify

= L (y (s) + s \frac{d}{d s} (y (s)))

Popular Examples

integral of 1/(2x^2-12x+26)

\int \frac{1}{2 x ^{2} - 12 x + 26} d x

integral of (1+arctan(x))/(1+x^2)

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

(\partial)/(\partial y)(1/2 (x-y)^2)

\frac{\partial}{\partial y} (\frac{1}{2} (x - y)^{2})

limit as x approaches 2 of x^2-4x+2

x \to 2 lim (x^{2} - 4 x + 2)

inverse oflaplace 1/(2s^2+s)inverse laplace

\frac{1}{2 s ^{2} + s}

Frequently Asked Questions (FAQ)

What is the d/(ds)(sL({y}(s))) ?
The d/(ds)(sL({y}(s))) is L({y}(s)+s d/(ds)({y}(s)))
What is the first d/(ds)(sL({y}(s))) ?
The first d/(ds)(sL({y}(s))) is L({y}(s)+s d/(ds)({y}(s)))