What is (\partial)/(\partial y)(8x^{5y}) ?

The answer to (\partial)/(\partial y)(8x^{5y}) is 40x^{5y}ln(x)

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(\partial)/(\partial y)(8x^{5y})

\frac{\partial}{\partial y} (8 x^{5 y})

40 x^{5 y} ln (x)

Solution steps

\frac{\partial}{\partial y} (8 x^{5 y})

Treat

x

as a constant

Take the constant out:

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

= 8 \frac{\partial}{\partial y} (x^{5 y})

Apply exponent rule:

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

x^{5 y} = e^{5 y l n (x)}

= 8 \frac{\partial}{\partial y} (e^{5 y l n (x)})

Apply the chain rule:

e^{5 y l n (x)} \frac{\partial}{\partial y} (5 y ln (x))

= e^{5 y l n (x)} \frac{\partial}{\partial y} (5 y ln (x))

\frac{\partial}{\partial y} (5 y ln (x)) = 5 ln (x)

= 8 e^{5 y l n (x)} \cdot 5 ln (x)

Simplify

8 e^{5 y l n (x)} \cdot 5 ln (x) : 40 x^{5 y} ln (x)

= 40 x^{5 y} ln (x)

\frac{d y}{d t} = 2 y (1 - \frac{y}{2})

\frac{d}{d x} (\frac{2 - x}{x + 1})

\frac{d y}{d x} = x + y + 1

d er i v a t i v e f (x) = (x + 1)^{3}

(\frac{x ^{2}}{100} + 8 + \frac{20}{x})^{^{'}}

What is (\partial)/(\partial y)(8x^{5y}) ?
The answer to (\partial)/(\partial y)(8x^{5y}) is 40x^{5y}ln(x)