What is the derivative of x^3y^2-3xsin(xy) ?

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

What is the first derivative of x^3y^2-3xsin(xy) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3 x sin (x y)) = 3 (sin (x y) + x cos (x y) (y + x \frac{d y}{d x}))

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

\frac{d}{d x} (\frac{1}{2 x} + 5 cos (x))

\frac{d}{d x} (- x^{2} + 6 x - 4)

\int n x^{n} d x

\int \frac{1}{x ^{2} 3 - x ^{2}} d x

x \to \infty lim (- 2 x)

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