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

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

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

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

- sin (x + e^{y})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= - sin (x + e^{y})

\int \frac{9 x}{x - 1} d x

y = 3 x^{2} - 12 x + 1, (0, 1)

f (x) = x^{2} + 2

\frac{d}{d x} (\frac{x ^{2} - 3}{x + 1})

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