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

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

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

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

z^{2} cos (2 x y) \cdot 2 y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

cos (2 x y) \frac{\partial}{\partial x} (2 x y)

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

\frac{\partial}{\partial x} (2 x y) = 2 y

= z^{2} cos (2 x y) \cdot 2 y

y^{^{'}} = y (x y^{3} + 3)

\int_{0}^{3} \frac{x}{x ^{2} + 6 x + 13} d x

3 y^{^{''}} - 5 y^{^{'}} - 2 y = t^{3} - 2 t

f (x) = sin^{2} (3 x)

\frac{d ^{2}}{d x ^{2}} (cos^{2} (5 π x))

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