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

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

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(\partial)/(\partial x)(x^{y^2})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Power Rule:

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

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

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

n = 1 \sum \infty \frac{1}{( 2 n + 1 ) ^{2}}

n = 1 \sum \infty \frac{4 n + 1}{4 ^{n + 1}}

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

\int sin^{3} (\frac{7}{3}) x d x

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