What is the derivative of x^ay^b ?

The derivative of x^ay^b is ax^{a-1}y^b+by^{b-1}(dy)/(dx)x^a

What is the first derivative of x^ay^b ?

The first derivative of x^ay^b is ax^{a-1}y^b+by^{b-1}(dy)/(dx)x^a

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\frac{d}{d x} (x^{a} y^{b})

a x^{a - 1} y^{b} + b y^{b - 1} \frac{d y}{d x} x^{a}

Solution steps

\frac{d}{d x} (x^{a} y^{b})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{a}, g = y^{b}

= \frac{d}{d x} (x^{a}) y^{b} + \frac{d}{d x} (y^{b}) x^{a}

\frac{d}{d x} (x^{a}) = a x^{a - 1}

\frac{d}{d x} (y^{b}) = b y^{b - 1} \frac{d y}{d x}

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

What is the derivative of x^ay^b ?
The derivative of x^ay^b is ax^{a-1}y^b+by^{b-1}(dy)/(dx)x^a
What is the first derivative of x^ay^b ?
The first derivative of x^ay^b is ax^{a-1}y^b+by^{b-1}(dy)/(dx)x^a