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)

\frac{d}{d x} ((x^{3} + 2 x) e^{s i n (x)})

f (x) = - \frac{1}{3} t^{3} + 64 t + 3000

y^{^{'}} = \frac{1 - y ^{2}}{y}

\int \frac{( x - 7 )}{x ^{2} - 18 x + 82} d x

x^{2} + 25

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)