What is (\partial)/(\partial y)(x^{4y}) ?

The answer to (\partial)/(\partial y)(x^{4y}) is 4x^{4y}ln(x)

(\partial)/(\partial y)(x^{4y})

\frac{\partial}{\partial y} (x^{4 y})

4 x^{4 y} ln (x)

Solution steps

\frac{\partial}{\partial y} (x^{4 y})

Treat

x

as a constant

Apply exponent rule:

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

x^{4 y} = e^{4 y l n (x)}

= \frac{\partial}{\partial y} (e^{4 y l n (x)})

Apply the chain rule:

e^{4 y l n (x)} \frac{\partial}{\partial y} (4 y ln (x))

= e^{4 y l n (x)} \frac{\partial}{\partial y} (4 y ln (x))

\frac{\partial}{\partial y} (4 y ln (x)) = 4 ln (x)

= e^{4 y l n (x)} \cdot 4 ln (x)

e^{4 y l n (x)} = x^{4 y}

= 4 x^{4 y} ln (x)

x \to - \infty lim (\frac{( 5 x ^{2} - 2 )}{x + 3})

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})

x \to 3 lim (4 x^{3} - 5 x^{2} + x - 8)

\int sec^{2} (x) - csc (x) cot (x) d x

x \to - 3 lim (f (x) x)

What is (\partial)/(\partial y)(x^{4y}) ?
The answer to (\partial)/(\partial y)(x^{4y}) is 4x^{4y}ln(x)