What is (\partial)/(\partial y)(3x^{3y}) ?

The answer to (\partial)/(\partial y)(3x^{3y}) is 9x^{3y}ln(x)

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(\partial)/(\partial y)(3x^{3y})

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

9 x^{3 y} ln (x)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 3 \frac{\partial}{\partial y} (x^{3 y})

Apply exponent rule:

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

x^{3 y} = e^{3 y l n (x)}

= 3 \frac{\partial}{\partial y} (e^{3 y l n (x)})

Apply the chain rule:

e^{3 y l n (x)} \frac{\partial}{\partial y} (3 y ln (x))

= e^{3 y l n (x)} \frac{\partial}{\partial y} (3 y ln (x))

\frac{\partial}{\partial y} (3 y ln (x)) = 3 ln (x)

= 3 e^{3 y l n (x)} \cdot 3 ln (x)

Simplify

3 e^{3 y l n (x)} \cdot 3 ln (x) : 9 x^{3 y} ln (x)

= 9 x^{3 y} ln (x)

\int (5 x - 4)^{2} d x

f (x) = (3 x + 5)^{3}

f (x) = \frac{5}{x + 2}

y = 4 x^{2}, y = x^{2} + 1

y^{^{'}} + 2 x y = x y^{2}

What is (\partial)/(\partial y)(3x^{3y}) ?
The answer to (\partial)/(\partial y)(3x^{3y}) is 9x^{3y}ln(x)