What is the derivative of x^4y^2 ?

The derivative of x^4y^2 is 4x^3y^2+2y(dy)/(dx)x^4

What is the first derivative of x^4y^2 ?

The first derivative of x^4y^2 is 4x^3y^2+2y(dy)/(dx)x^4

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\frac{d}{d x} (x^{4} y^{2})

4 x^{3} y^{2} + 2 y \frac{d y}{d x} x^{4}

Solution steps

\frac{d}{d x} (x^{4} y^{2})

Apply the Product Rule:

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

f = x^{4}, g = y^{2}

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} y^{2} + 2 y \frac{d y}{d x} x^{4}

\frac{d}{d x} (\frac{2 x ^{2} + 1}{x})

\int 6 e^{4 t a n (2 x)} sec^{2} (2 x) d x

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

\int \frac{x}{1 + 2 x} d x

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

What is the derivative of x^4y^2 ?
The derivative of x^4y^2 is 4x^3y^2+2y(dy)/(dx)x^4
What is the first derivative of x^4y^2 ?
The first derivative of x^4y^2 is 4x^3y^2+2y(dy)/(dx)x^4