What is (\partial)/(\partial x)(a(mx)^b(my)^{1-b}) ?

The answer to (\partial)/(\partial x)(a(mx)^b(my)^{1-b}) is ambx^{b-1}y^{1-b}

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(\partial)/(\partial x)(a(mx)^b(my)^{1-b})

\frac{\partial}{\partial x} (a (m x)^{b} (m y)^{1 - b})

amb x^{b - 1} y^{1 - b}

Solution steps

\frac{\partial}{\partial x} (a (m x)^{b} (m y)^{1 - b})

Treat

a, m, b, y

as constants

Take the constant out:

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

= a (m y)^{1 - b} \frac{\partial}{\partial x} ((m x)^{b})

Apply the chain rule:

b (m x)^{b - 1} \frac{\partial}{\partial x} (m x)

= b (m x)^{b - 1} \frac{\partial}{\partial x} (m x)

\frac{\partial}{\partial x} (m x) = m

= a (m y)^{1 - b} b (m x)^{b - 1} m

Simplify

a (m y)^{1 - b} b (m x)^{b - 1} m : amb x^{b - 1} y^{1 - b}

= amb x^{b - 1} y^{1 - b}

\frac{d ^{2} x}{d t ^{2}} - 4 \frac{d x}{d t} + 4 x = 2 t

\int (3 x + 2)^{3} d x

x^{\frac{2}{3}} (1 - x)

\int \frac{x + 1}{x - 1} d x

What is (\partial)/(\partial x)(a(mx)^b(my)^{1-b}) ?
The answer to (\partial)/(\partial x)(a(mx)^b(my)^{1-b}) is ambx^{b-1}y^{1-b}