What is the derivative of x^5y^2 ?

The derivative of x^5y^2 is 5x^4y^2+2y(dy)/(dx)x^5

What is the first derivative of x^5y^2 ?

The first derivative of x^5y^2 is 5x^4y^2+2y(dy)/(dx)x^5

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\frac{d}{d x} (x^{5} y^{2})

5 x^{4} y^{2} + 2 y \frac{d y}{d x} x^{5}

Solution steps

\frac{d}{d x} (x^{5} y^{2})

Apply the Product Rule:

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

f = x^{5}, g = y^{2}

= \frac{d}{d x} (x^{5}) y^{2} + \frac{d}{d x} (y^{2}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

= 5 x^{4} y^{2} + 2 y \frac{d y}{d x} x^{5}

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

\int_{0}^{4} \frac{1}{( 6 - 2 x ) ^{\frac{1}{3}}} d x

(\frac{y ^{^{'}} - e ^{- t} + 5}{y}) = - 5, y (0) = - 2

\int \frac{5}{9 - ( x - 3 ) ^{2}} d x

y = \frac{2}{x - 4}

What is the derivative of x^5y^2 ?
The derivative of x^5y^2 is 5x^4y^2+2y(dy)/(dx)x^5
What is the first derivative of x^5y^2 ?
The first derivative of x^5y^2 is 5x^4y^2+2y(dy)/(dx)x^5