What is (\partial)/(\partial y)(7e^{x^2ln(y)}) ?

The answer to (\partial)/(\partial y)(7e^{x^2ln(y)}) is 7x^2y^{x^2-1}

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(\partial)/(\partial y)(7e^{x^2ln(y)})

\frac{\partial}{\partial y} (7 e^{x^{2} l n (y)})

7 x^{2} y^{x^{2} - 1}

Solution steps

\frac{\partial}{\partial y} (7 e^{x^{2} l n (y)})

Simplify

7 e^{x^{2} l n (y)} : 7 y^{x^{2}}

= \frac{\partial}{\partial y} (7 y^{x^{2}})

Treat

x

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial y} (y^{x^{2}})

Apply the Power Rule:

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

= 7 x^{2} y^{x^{2} - 1}

5 Y^{\frac{5}{8}} X^{\frac{3}{8}}

\int \frac{1}{3 x + 12} d x

\frac{\partial}{\partial y} (e^{x + y + 4})

\frac{d y}{d x} = 3 y + 1

\frac{d}{d x} (2 + cos (2 x))

What is (\partial)/(\partial y)(7e^{x^2ln(y)}) ?
The answer to (\partial)/(\partial y)(7e^{x^2ln(y)}) is 7x^2y^{x^2-1}