What is (\partial)/(\partial y)(9x^{6y}) ?

The answer to (\partial)/(\partial y)(9x^{6y}) is 54x^{6y}ln(x)

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(\partial)/(\partial y)(9x^{6y})

\frac{\partial}{\partial y} (9 x^{6 y})

54 x^{6 y} ln (x)

Solution steps

\frac{\partial}{\partial y} (9 x^{6 y})

Treat

x

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial y} (x^{6 y})

Apply exponent rule:

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

x^{6 y} = e^{6 y l n (x)}

= 9 \frac{\partial}{\partial y} (e^{6 y l n (x)})

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (6 y ln (x)) = 6 ln (x)

= 9 e^{6 y l n (x)} \cdot 6 ln (x)

Simplify

9 e^{6 y l n (x)} \cdot 6 ln (x) : 54 x^{6 y} ln (x)

= 54 x^{6 y} ln (x)

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

\frac{d y}{d t} = yr (1000 - y)

y = sec^{2} (x), y = 8 cos (x), - \frac{π}{3}, \frac{π}{3}

\int_{1}^{\infty} \frac{ln ( x )}{x ^{\frac{3}{2}}} d x

\frac{d}{d x} (1000 (1 + \frac{x}{12})^{60})

What is (\partial)/(\partial y)(9x^{6y}) ?
The answer to (\partial)/(\partial y)(9x^{6y}) is 54x^{6y}ln(x)