What is (\partial)/(\partial x)(sin(5xy+4yz+7xz)) ?

The answer to (\partial)/(\partial x)(sin(5xy+4yz+7xz)) is cos(5xy+4yz+7xz)(5y+7z)

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(\partial)/(\partial x)(sin(5xy+4yz+7xz))

\frac{\partial}{\partial x} (sin (5 x y + 4 yz + 7 x z))

cos (5 x y + 4 yz + 7 x z) (5 y + 7 z)

Solution steps

\frac{\partial}{\partial x} (sin (5 x y + 4 yz + 7 x z))

Treat

y, z

as constants

Apply the chain rule:

cos (5 x y + 4 yz + 7 x z) \frac{\partial}{\partial x} (5 x y + 4 yz + 7 x z)

= cos (5 x y + 4 yz + 7 x z) \frac{\partial}{\partial x} (5 x y + 4 yz + 7 x z)

\frac{\partial}{\partial x} (5 x y + 4 yz + 7 x z) = 5 y + 7 z

= cos (5 x y + 4 yz + 7 x z) (5 y + 7 z)

f (x) = \frac{- 8 x}{x ^{2} + 1}, (0, 0)

\int_{2}^{5} x d x

\int e^{- \frac{1}{2} z^{2}}

\frac{d x}{d t} = 0.6 - \frac{5 x}{1000 + t}

y = ln (x + 4)

What is (\partial)/(\partial x)(sin(5xy+4yz+7xz)) ?
The answer to (\partial)/(\partial x)(sin(5xy+4yz+7xz)) is cos(5xy+4yz+7xz)(5y+7z)