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

The answer to (\partial)/(\partial x)(x^{nxy}) is nyx^{nxy}(ln(x)+1)

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(\partial)/(\partial x)(x^{nxy})

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

n y x^{n x y} (ln (x) + 1)

Solution steps

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

Treat

n, y

as a constant

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{n x y} = e^{n x y l n (x)}

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

Apply the chain rule:

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

= e^{n x y l n (x)} \frac{\partial}{\partial x} (n x y ln (x))

\frac{\partial}{\partial x} (n x y ln (x)) = y n (ln (x) + 1)

= e^{n x y l n (x)} y n (ln (x) + 1)

e^{n x y l n (x)} = x^{n x y}

= n y x^{n x y} (ln (x) + 1)

\frac{d}{d x} (9 x^{2})

\int e^{i 6 x} cos (3 x) d x

\int - cos (x) 3 x^{2} d x

\int \frac{1}{3 x + 6} d x

x \to 1 - lim (\frac{1}{x - 1})

What is (\partial)/(\partial x)(x^{nxy}) ?
The answer to (\partial)/(\partial x)(x^{nxy}) is nyx^{nxy}(ln(x)+1)