What is (\partial)/(\partial x)(7e^{xy}*cos(xyz)) ?

The answer to (\partial)/(\partial x)(7e^{xy}*cos(xyz)) is 7(e^{xy}ycos(xyz)-e^{xy}yzsin(xyz))

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(\partial)/(\partial x)(7e^{xy}*cos(xyz))

\frac{\partial}{\partial x} (7 e^{x y} \cdot cos (x yz))

7 (e^{x y} y cos (x yz) - e^{x y} yz sin (x yz))

Solution steps

\frac{\partial}{\partial x} (7 e^{x y} cos (x yz))

Treat

y, z

as constants

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (e^{x y} cos (x yz))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x y}, g = cos (x yz)

= 7 (\frac{\partial}{\partial x} (e^{x y}) cos (x yz) + \frac{\partial}{\partial x} (cos (x yz)) e^{x y})

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

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

= 7 (e^{x y} y cos (x yz) + (- sin (x yz) yz) e^{x y})

Simplify

= 7 (e^{x y} y cos (x yz) - e^{x y} yz sin (x yz))

x \to 0 lim (\frac{f ( x )}{x})

\frac{d y}{d x} = y (1000 - y)

y = 5 e^{- x}, (0, 5)

\frac{2}{( s ^{2} - 3 )} - 3 \frac{s}{( s ^{2} - 3 )}

\int (\frac{20}{1 + x ^{2}}) d x

What is (\partial)/(\partial x)(7e^{xy}*cos(xyz)) ?
The answer to (\partial)/(\partial x)(7e^{xy}*cos(xyz)) is 7(e^{xy}ycos(xyz)-e^{xy}yzsin(xyz))