What is (\partial)/(\partial x)(sin(x+e^y)) ?

The answer to (\partial)/(\partial x)(sin(x+e^y)) is cos(x+e^y)

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(\partial)/(\partial x)(sin(x+e^y))

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

cos (x + e^{y})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

cos (x + e^{y}) \frac{\partial}{\partial x} (x + e^{y})

= cos (x + e^{y}) \frac{\partial}{\partial x} (x + e^{y})

\frac{\partial}{\partial x} (x + e^{y}) = 1

= cos (x + e^{y}) \cdot 1

Simplify

= cos (x + e^{y})

8 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

\int (5 - 3 x)^{7} d x

\int 2 x^{- 5} d x

\frac{\partial}{\partial y} (5 y - e^{8 s i n (x)})

n = 6 \sum \infty \frac{1}{n ^{2} - 4}

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