What is (\partial)/(\partial y)(8e^{yz}cos(xyz)) ?

The answer to (\partial)/(\partial y)(8e^{yz}cos(xyz)) is 8(e^{yz}zcos(yzx)-e^{yz}zxsin(yzx))

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(\partial)/(\partial y)(8e^{yz}cos(xyz))

\frac{\partial}{\partial y} (8 e^{yz} cos (x yz))

8 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

Solution steps

\frac{\partial}{\partial y} (8 e^{yz} cos (x yz))

Treat

z, x

as constants

Take the constant out:

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

= 8 \frac{\partial}{\partial y} (e^{yz} cos (x yz))

Apply the Product Rule:

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

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

= 8 (\frac{\partial}{\partial y} (e^{yz}) cos (x yz) + \frac{\partial}{\partial y} (cos (x yz)) e^{yz})

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

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

= 8 (e^{yz} z cos (x yz) + (- sin (x yz) z x) e^{yz})

Simplify

= 8 (e^{yz} z cos (yz x) - e^{yz} z x sin (yz x))

(4.8) (2.12)

\frac{d}{d x} (x e^{2 x})

\int sin^{2} (\frac{π}{4} + \frac{t}{2}) d t

x \to - 7 lim (x^{2} - 49)

\frac{1}{t ^{2} + 5 t - 1}

What is (\partial)/(\partial y)(8e^{yz}cos(xyz)) ?
The answer to (\partial)/(\partial y)(8e^{yz}cos(xyz)) is 8(e^{yz}zcos(yzx)-e^{yz}zxsin(yzx))