What is (\partial)/(\partial x)(sin(x+xy+z^2)) ?

The answer to (\partial)/(\partial x)(sin(x+xy+z^2)) is cos(x+xy+z^2)(y+1)

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(\partial)/(\partial x)(sin(x+xy+z^2))

\frac{\partial}{\partial x} (sin (x + x y + z^{2}))

cos (x + x y + z^{2}) (y + 1)

Solution steps

\frac{\partial}{\partial x} (sin (x + x y + z^{2}))

Treat

y, z

as constants

Apply the chain rule:

cos (x + x y + z^{2}) \frac{\partial}{\partial x} (x + x y + z^{2})

= cos (x + x y + z^{2}) \frac{\partial}{\partial x} (x + x y + z^{2})

\frac{\partial}{\partial x} (x + x y + z^{2}) = y + 1

= cos (x + x y + z^{2}) (y + 1)

\frac{\partial}{\partial x} (y^{4} cos (5 x))

\int_{5}^{8} \frac{1}{9 + ( x - 5 ) ^{2}} d x

n = 1 \sum \infty 2^{n + 1} - 2^{n}

n = 0 \sum \infty (sin (8))^{n}

\frac{d}{d x} (\frac{( 4 x - 2 ) ^{4}}{( - 5 x + 1 ) ^{5}})

What is (\partial)/(\partial x)(sin(x+xy+z^2)) ?
The answer to (\partial)/(\partial x)(sin(x+xy+z^2)) is cos(x+xy+z^2)(y+1)