What is (\partial)/(\partial y)(6x^{2y}) ?

The answer to (\partial)/(\partial y)(6x^{2y}) is 12x^{2y}ln(x)

(\partial)/(\partial y)(6x^{2y})

\frac{\partial}{\partial y} (6 x^{2 y})

12 x^{2 y} ln (x)

Solution steps

\frac{\partial}{\partial y} (6 x^{2 y})

Treat

x

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial y} (x^{2 y})

Apply exponent rule:

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

x^{2 y} = e^{2 y l n (x)}

= 6 \frac{\partial}{\partial y} (e^{2 y l n (x)})

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (2 y ln (x)) = 2 ln (x)

= 6 e^{2 y l n (x)} \cdot 2 ln (x)

Simplify

6 e^{2 y l n (x)} \cdot 2 ln (x) : 12 x^{2 y} ln (x)

= 12 x^{2 y} ln (x)

(x^{2} - 1) y^{^{'}} + 2 x y^{2} = 0, y (0) = 1

\frac{d}{d x} (sin (x^{2} + e^{x}))

\int_{0}^{π} 3 sin (x) d x

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\frac{\partial}{\partial x} (7 sin (x) sin (y))

What is (\partial)/(\partial y)(6x^{2y}) ?
The answer to (\partial)/(\partial y)(6x^{2y}) is 12x^{2y}ln(x)