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

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

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

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

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

Solution steps

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

Treat

c, t

as a constant

Apply the chain rule:

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

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

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

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

t \frac{d y}{d t} = t^{3} + 11 t^{3} y

\frac{d}{d x} (lo g_{7} (6 x - 5))

\int (x 1 - x^{2}) d x

3 x^{2} cos (2 x)

x \to 7 - lim (\frac{4 x}{x - 7})

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