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

The answer to (\partial)/(\partial x)(zsin(xy^2+2z)) is zcos(xy^2+2z)y^2

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

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

\frac{\partial}{\partial x} (x y + z^{3} x - 2 yz)

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

\int_{- 1}^{2} (x + 2 - x^{2})^{2} d x

t \to 1 lim (f (t))

y^{^{''}} + 16 y = 5 sec (4 t)

What is (\partial)/(\partial x)(zsin(xy^2+2z)) ?
The answer to (\partial)/(\partial x)(zsin(xy^2+2z)) is zcos(xy^2+2z)y^2