What is the derivative of x^3+xy^2 ?

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

What is the first derivative of x^3+xy^2 ?

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

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\frac{d}{d x} (x^{3} + x y^{2})

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

Solution steps

\frac{d}{d x} (x^{3} + x y^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

d er i v a t i v e e^{- x^{5}}

\int (u + 3) (8 u + 5) d u

\int \frac{e ^{4 x}}{( e ^{2 x} - 1 ) ^{3}} d x

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

x \to 0 lim (\frac{x}{x ^{2} - 4 x})

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