What is (\partial)/(\partial x)(e^{x-1}cos(y)) ?

The answer to (\partial)/(\partial x)(e^{x-1}cos(y)) is e^{x-1}cos(y)

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(\partial)/(\partial x)(e^{x-1}cos(y))

\frac{\partial}{\partial x} (e^{x - 1} cos (y))

e^{x - 1} cos (y)

Solution steps

\frac{\partial}{\partial x} (e^{x - 1} cos (y))

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{x - 1} \frac{\partial}{\partial x} (x - 1)

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

\frac{\partial}{\partial x} (x - 1) = 1

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

Simplify

= e^{x - 1} cos (y)

\frac{d}{d x} (cos^{4} (sin^{3} (x)))

y = arccos (5 x)

\frac{d}{d x} (\frac{4}{x + 3})

\frac{d}{d x} (3 x - e^{x})

\frac{d y}{d x} - \frac{y}{x} = 1 - \frac{1}{x}

What is (\partial)/(\partial x)(e^{x-1}cos(y)) ?
The answer to (\partial)/(\partial x)(e^{x-1}cos(y)) is e^{x-1}cos(y)