What is (\partial)/(\partial x)(sin(5xy+8yz+9xz)) ?

The answer to (\partial)/(\partial x)(sin(5xy+8yz+9xz)) is cos(5xy+8yz+9xz)(5y+9z)

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(\partial)/(\partial x)(sin(5xy+8yz+9xz))

\frac{\partial}{\partial x} (sin (5 x y + 8 yz + 9 x z))

cos (5 x y + 8 yz + 9 x z) (5 y + 9 z)

Solution steps

\frac{\partial}{\partial x} (sin (5 x y + 8 yz + 9 x z))

Treat

y, z

as constants

Apply the chain rule:

cos (5 x y + 8 yz + 9 x z) \frac{\partial}{\partial x} (5 x y + 8 yz + 9 x z)

= cos (5 x y + 8 yz + 9 x z) \frac{\partial}{\partial x} (5 x y + 8 yz + 9 x z)

\frac{\partial}{\partial x} (5 x y + 8 yz + 9 x z) = 5 y + 9 z

= cos (5 x y + 8 yz + 9 x z) (5 y + 9 z)

What is (\partial)/(\partial x)(sin(5xy+8yz+9xz)) ?
The answer to (\partial)/(\partial x)(sin(5xy+8yz+9xz)) is cos(5xy+8yz+9xz)(5y+9z)