What is the derivative of x^2*y-4x^3+3*4^2 ?

The derivative of x^2*y-4x^3+3*4^2 is x^2(dy)/(dx)-12x^2+2xy

What is the first derivative of x^2*y-4x^3+3*4^2 ?

The first derivative of x^2*y-4x^3+3*4^2 is x^2(dy)/(dx)-12x^2+2xy

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\frac{d}{d x} (x^{2} \cdot y - 4 x^{3} + 3 \cdot 4^{2})

x^{2} \frac{d y}{d x} - 12 x^{2} + 2 x y

Solution steps

\frac{d}{d x} (x^{2} y - 4 x^{3} + 3 \cdot 4^{2})

Simplify

x^{2} y - 4 x^{3} + 3 \cdot 4^{2} : x^{2} y - 4 x^{3} + 48

= \frac{d}{d x} (x^{2} y - 4 x^{3} + 48)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2} y) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (48)

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (48) = 0

= 2 x y + \frac{d y}{d x} x^{2} - 12 x^{2} + 0

Simplify

= x^{2} \frac{d y}{d x} - 12 x^{2} + 2 x y

What is the derivative of x^2*y-4x^3+3*4^2 ?
The derivative of x^2*y-4x^3+3*4^2 is x^2(dy)/(dx)-12x^2+2xy
What is the first derivative of x^2*y-4x^3+3*4^2 ?
The first derivative of x^2*y-4x^3+3*4^2 is x^2(dy)/(dx)-12x^2+2xy