What is (\partial)/(\partial y)(9x^{8y}) ?

The answer to (\partial)/(\partial y)(9x^{8y}) is 72x^{8y}ln(x)

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(\partial)/(\partial y)(9x^{8y})

\frac{\partial}{\partial y} (9 x^{8 y})

72 x^{8 y} ln (x)

Solution steps

\frac{\partial}{\partial y} (9 x^{8 y})

Treat

x

as a constant

Take the constant out:

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

= 9 \frac{\partial}{\partial y} (x^{8 y})

Apply exponent rule:

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

x^{8 y} = e^{8 y l n (x)}

= 9 \frac{\partial}{\partial y} (e^{8 y l n (x)})

Apply the chain rule:

e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

= e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

\frac{\partial}{\partial y} (8 y ln (x)) = 8 ln (x)

= 9 e^{8 y l n (x)} \cdot 8 ln (x)

Simplify

9 e^{8 y l n (x)} \cdot 8 ln (x) : 72 x^{8 y} ln (x)

= 72 x^{8 y} ln (x)

f (x) = (x - 1)^{2} (x - 2)^{3}

\int (2 x^{2} + \frac{1}{( 4 x ) ^{2}}) d x

\frac{d}{d y} (\frac{x}{2 y ^{4}})

\frac{\partial}{\partial z} (x cos (y))

x \to 0 + lim ((1 - x)^{(\frac{1}{x})})

What is (\partial)/(\partial y)(9x^{8y}) ?
The answer to (\partial)/(\partial y)(9x^{8y}) is 72x^{8y}ln(x)