What is (\partial)/(\partial x)(x^2ycos(z/t)) ?

The answer to (\partial)/(\partial x)(x^2ycos(z/t)) is 2xycos(z/t)

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(\partial)/(\partial x)(x^2ycos(z/t))

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

2 x y cos (\frac{z}{t})

Solution steps

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

Treat

y, z, t

as constants

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y cos (\frac{z}{t}) \cdot 2 x^{2 - 1}

Simplify

= 2 x y cos (\frac{z}{t})

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

\frac{\partial}{\partial x} (e^{2^{x}})

y^{^{'}} = 20 x - 2

\frac{d}{d x} (2 x + e^{x} + e^{- x})

F (x) = sin (7 x) + cos (4 x)

What is (\partial)/(\partial x)(x^2ycos(z/t)) ?
The answer to (\partial)/(\partial x)(x^2ycos(z/t)) is 2xycos(z/t)