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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

cos (x)

\int_{1}^{3} x + 2 d x

3 y^{^{'}} + 12 y = 4

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

2 x^{2} - 2 x + C

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