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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

f (x) = x^{3} - 18 x y + y^{3}

2 x - 13

0.2329 sin (s) + 0.957 cos (s) - 1

7 x e^{- x}

f (x) = (9 x^{2} + 1) [- 1.2]

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