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

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

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

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

6 x^{6 y} ln (x)

Solution steps

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

Treat

x

as a constant

Apply exponent rule:

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

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

= \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)

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

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

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

f (x) = 2 x - 3

f (x) = (1 + 3 x^{4})^{2} + 3 x^{3}

y^{^{''}} + y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

\frac{8}{s ^{2} + 1}

\frac{1}{y} d y = \frac{x + 1}{1 - x ^{2}} d x

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