What is (\partial)/(\partial y)(tan(x)y^{2.5}) ?

The answer to (\partial)/(\partial y)(tan(x)y^{2.5}) is 2.5y^{1.5}tan(x)

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(\partial)/(\partial y)(tan(x)y^{2.5})

\frac{\partial}{\partial y} (tan (x) y^{2.5})

2.5 y^{1.5} tan (x)

Solution steps

\frac{\partial}{\partial y} (tan (x) y^{2.5})

Treat

x

as a constant

Take the constant out:

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

= tan (x) \frac{\partial}{\partial y} (y^{2.5})

Apply the Power Rule:

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

= tan (x) \cdot 2.5 y^{2.5 - 1}

Simplify

= 2.5 y^{1.5} tan (x)

What is (\partial)/(\partial y)(tan(x)y^{2.5}) ?
The answer to (\partial)/(\partial y)(tan(x)y^{2.5}) is 2.5y^{1.5}tan(x)