What is (\partial)/(\partial x)(sin(w/c x)sin(wt)) ?

The answer to (\partial)/(\partial x)(sin(w/c x)sin(wt)) is (wsin(wt)cos((wx)/c))/(c)

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(\partial)/(\partial x)(sin(w/c x)sin(wt))

\frac{\partial}{\partial x} (sin (\frac{w}{c} x) sin (wt))

\frac{w sin ( wt ) cos ( \frac{w x}{c} )}{c}

Solution steps

\frac{\partial}{\partial x} (sin (\frac{w}{c} x) sin (wt))

Simplify

sin (\frac{w}{c} x) sin (wt) : sin (wt) sin (\frac{w x}{c})

= \frac{\partial}{\partial x} (sin (wt) sin (\frac{w x}{c}))

Treat

c, w, t

as constants

Take the constant out:

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

= sin (wt) \frac{\partial}{\partial x} (sin (\frac{w x}{c}))

Apply the chain rule:

cos (\frac{w x}{c}) \frac{\partial}{\partial x} (\frac{w x}{c})

= cos (\frac{w x}{c}) \frac{\partial}{\partial x} (\frac{w x}{c})

\frac{\partial}{\partial x} (\frac{w x}{c}) = \frac{w}{c}

= sin (wt) cos (\frac{w x}{c}) \frac{w}{c}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{w sin ( wt ) cos ( \frac{w x}{c} )}{c}

t \to 0 lim (\frac{4 e ^{t} - 4}{t})

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

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

\frac{\partial}{\partial y} (ln (x^{3} + 1) + y^{2})

\int_{- 2}^{- 1} 15 x^{- 4} d x

What is (\partial)/(\partial x)(sin(w/c x)sin(wt)) ?
The answer to (\partial)/(\partial x)(sin(w/c x)sin(wt)) is (wsin(wt)cos((wx)/c))/(c)