What is (\partial)/(\partial y)(7e^{yz}cos(xyz)) ?

The answer to (\partial)/(\partial y)(7e^{yz}cos(xyz)) is 7(e^{yz}zcos(yzx)-e^{yz}zxsin(yzx))

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(\partial)/(\partial y)(7e^{yz}cos(xyz))

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

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

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

= 7 \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)

= 7 (\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

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

Simplify

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

\frac{d}{d x} (x + x + 7)

\frac{d}{d x} (\frac{( x + 2 ) ( x ^{2} - 2 x + 4 )}{x ^{3}})

\int \frac{1}{x ^{2} x ^{2} - 169} d x

\int \frac{1 - x ^{2}}{x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 20 y = 80

What is (\partial)/(\partial y)(7e^{yz}cos(xyz)) ?
The answer to (\partial)/(\partial y)(7e^{yz}cos(xyz)) is 7(e^{yz}zcos(yzx)-e^{yz}zxsin(yzx))