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

The answer to (\partial)/(\partial x)(cos(x)cos(y)e^z) is -e^zsin(x)cos(y)

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

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

- e^{z} sin (x) cos (y)

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial x} (cos (x)) = - sin (x)

= cos (y) e^{z} (- sin (x))

Simplify

= - e^{z} sin (x) cos (y)

\int \frac{1}{( x - 7 ) ^{2}} d x

y^{^{''}} - 5 y^{^{'}} - 6 y = 12 e^{2 t}

x \to 0 lim (\frac{1}{( x - 1 ) ^{2}} + 2)

\frac{d y}{d x} + 10 y = 11

\frac{d}{d x} (x^{2} - 4 x + 10)

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