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

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

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

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

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

Solution steps

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

Treat

c, t

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\frac{( x + 1 ) d y}{d x} + (x + 2) y = 2 x e^{- x}

\int \frac{c}{x} d x

x \to 0.1 lim (\frac{e ^{5 x} - 1}{x})

4 y^{^{''}} + 36 y^{^{'}} + 81 y = 0

t an g e n t - 3 x^{2} + 6 x - 2

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