What is (\partial)/(\partial t)(3e^{sin(x+4ct)}) ?

The answer to (\partial)/(\partial t)(3e^{sin(x+4ct)}) is 12ce^{sin(x+4ct)}cos(x+4ct)

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(\partial)/(\partial t)(3e^{sin(x+4ct)})

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})

12 c e^{s i n (x + 4 c t)} cos (x + 4 c t)

Solution steps

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})

Treat

c, x

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial t} (e^{s i n (x + 4 c t)})

Apply the chain rule:

e^{s i n (x + 4 c t)} \frac{\partial}{\partial t} (sin (x + 4 c t))

= e^{s i n (x + 4 c t)} \frac{\partial}{\partial t} (sin (x + 4 c t))

\frac{\partial}{\partial t} (sin (x + 4 c t)) = cos (x + 4 c t) \cdot 4 c

= 3 e^{s i n (x + 4 c t)} cos (x + 4 c t) \cdot 4 c

Simplify

= 12 c e^{s i n (x + 4 c t)} cos (x + 4 c t)

f (x) = x^{6 x}

y^{^{'}} = \frac{( 4 x ^{3} + y ^{3} )}{x y ^{2}}

n = 0 \sum \infty \frac{1}{2 n !}

y^{^{'}} = cos^{2} (y) ln (x)

\frac{\partial}{\partial x} (e^{5 x} sin (5 y))

What is (\partial)/(\partial t)(3e^{sin(x+4ct)}) ?
The answer to (\partial)/(\partial t)(3e^{sin(x+4ct)}) is 12ce^{sin(x+4ct)}cos(x+4ct)