What is (\partial)/(\partial t)(e^{sin(x+ct)}) ?

The answer to (\partial)/(\partial t)(e^{sin(x+ct)}) is e^{sin(x+ct)}cos(x+ct)c

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(\partial)/(\partial t)(e^{sin(x+ct)})

\frac{\partial}{\partial t} (e^{s i n (x + c t)})

e^{s i n (x + c t)} cos (x + c t) c

Solution steps

\frac{\partial}{\partial t} (e^{s i n (x + c t)})

Treat

c, x

as a constant

Apply the chain rule:

e^{s i n (x + c t)} \frac{\partial}{\partial t} (sin (x + c t))

= e^{s i n (x + c t)} \frac{\partial}{\partial t} (sin (x + c t))

\frac{\partial}{\partial t} (sin (x + c t)) = cos (x + c t) c

= e^{s i n (x + c t)} cos (x + c t) c

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{- \frac{1}{2}}

\int 2 cos (x) sin (x) d x

\frac{d}{d x} (14.8 sin (\frac{π}{6} \cdot x - \frac{π}{2}) + 10)

\int (2 x^{3} + 2 x - 3) d x

\frac{\partial}{\partial x} (9 x cos (x) cos (y))

What is (\partial)/(\partial t)(e^{sin(x+ct)}) ?
The answer to (\partial)/(\partial t)(e^{sin(x+ct)}) is e^{sin(x+ct)}cos(x+ct)c