What is (\partial)/(\partial x)(e-4tcos(pix)) ?

The answer to (\partial)/(\partial x)(e-4tcos(pix)) is 4pitsin(pix)

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(\partial)/(\partial x)(e-4tcos(pix))

\frac{\partial}{\partial x} (e - 4 t cos (π x))

4 π t sin (π x)

Solution steps

\frac{\partial}{\partial x} (e - 4 t cos (π x))

Treat

t

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (e) - \frac{\partial}{\partial x} (4 t cos (π x))

\frac{\partial}{\partial x} (e) = 0

\frac{\partial}{\partial x} (4 t cos (π x)) = - 4 π t sin (π x)

= 0 - (- 4 π t sin (π x))

Simplify

= 4 π t sin (π x)

What is (\partial)/(\partial x)(e-4tcos(pix)) ?
The answer to (\partial)/(\partial x)(e-4tcos(pix)) is 4pitsin(pix)