What is the derivative of x^my^n ?

The derivative of x^my^n is mx^{m-1}y^n+ny(x)^{n-1}(dy)/(dx)x^m

What is the first derivative of x^my^n ?

The first derivative of x^my^n is mx^{m-1}y^n+ny(x)^{n-1}(dy)/(dx)x^m

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\frac{d}{d x} (x^{m} y^{n})

m x^{m - 1} y^{n} + n y (x)^{n - 1} \frac{d y}{d x} x^{m}

Solution steps

\frac{d}{d x} (x^{m} y^{n})

Apply the Product Rule:

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

f = x^{m}, g = y^{n}

= \frac{d}{d x} (x^{m}) y^{n} + \frac{d}{d x} (y^{n}) x^{m}

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

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

= m x^{m - 1} y^{n} + n y (x)^{n - 1} \frac{d y}{d x} x^{m}

(6, - 9), (- 2, - 1)

2 x y + x^{2} y^{^{'}} = y^{2}

\int y^{2} (7 - y^{3})^{\frac{2}{3}} d y

9 (x^{2} + 5 x)^{2} (2 x + 5)

y = \frac{16}{x}

What is the derivative of x^my^n ?
The derivative of x^my^n is mx^{m-1}y^n+ny(x)^{n-1}(dy)/(dx)x^m
What is the first derivative of x^my^n ?
The first derivative of x^my^n is mx^{m-1}y^n+ny(x)^{n-1}(dy)/(dx)x^m