What is (\partial)/(\partial y)(x^{7y}) ?

The answer to (\partial)/(\partial y)(x^{7y}) is 7x^{7y}ln(x)

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(\partial)/(\partial y)(x^{7y})

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

7 x^{7 y} ln (x)

Solution steps

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

Treat

x

as a constant

Apply exponent rule:

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

x^{7 y} = e^{7 y l n (x)}

= \frac{\partial}{\partial y} (e^{7 y l n (x)})

Apply the chain rule:

e^{7 y l n (x)} \frac{\partial}{\partial y} (7 y ln (x))

= e^{7 y l n (x)} \frac{\partial}{\partial y} (7 y ln (x))

\frac{\partial}{\partial y} (7 y ln (x)) = 7 ln (x)

= e^{7 y l n (x)} \cdot 7 ln (x)

e^{7 y l n (x)} = x^{7 y}

= 7 x^{7 y} ln (x)

\frac{d}{d x} (ln (- 2 x))

\int - \frac{8 x ^{3}}{( 5 - 2 x ^{4} ) ^{4}} d x

(3 x + 2)^{^{'}}

\frac{d}{d x} (x^{5} + x^{4})

10 y^{^{''}} - y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 0

What is (\partial)/(\partial y)(x^{7y}) ?
The answer to (\partial)/(\partial y)(x^{7y}) is 7x^{7y}ln(x)