What is the derivative of w*sin(wct*cos(wx)) ?

The derivative of w*sin(wct*cos(wx)) is -w^2sin(wx)sin(cwt)

What is the first derivative of w*sin(wct*cos(wx)) ?

The first derivative of w*sin(wct*cos(wx)) is -w^2sin(wx)sin(cwt)

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\frac{d}{d x} (w \cdot sin (w c t) \cdot cos (w x))

- w^{2} sin (w x) sin (c wt)

Solution steps

\frac{d}{d x} (w sin (w c t) cos (w x))

Treat

c, w, t

as constants

Take the constant out:

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

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

Apply the chain rule:

- sin (w x) \frac{d}{d x} (w x)

= - sin (w x) \frac{d}{d x} (w x)

\frac{d}{d x} (w x) = w

= w sin (w c t) (- sin (w x) w)

Simplify

w sin (w c t) (- sin (w x) w) : - w^{2} sin (w x) sin (c wt)

= - w^{2} sin (w x) sin (c wt)

\frac{\partial}{\partial x} (\frac{3}{x})

\frac{d x}{d t} = - 3 x (x^{2} - 1)

\int \frac{sin ( \frac{π}{x} )}{x ^{2}} d x

\frac{d y}{d t} = \frac{t ^{2}}{y ( 2 + t ^{3} )}

\frac{d}{d x} (sin (\frac{π}{2}))

What is the derivative of w*sin(wct*cos(wx)) ?
The derivative of w*sin(wct*cos(wx)) is -w^2sin(wx)sin(cwt)
What is the first derivative of w*sin(wct*cos(wx)) ?
The first derivative of w*sin(wct*cos(wx)) is -w^2sin(wx)sin(cwt)