What is the derivative of-xsin(xy) ?

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

What is the first derivative of-xsin(xy) ?

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

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\frac{d}{d x} (- x sin (x y))

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

Solution steps

\frac{d}{d x} (- x sin (x y))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x y)

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

\frac{d x}{d x} = 1

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

= - (1 \cdot sin (x y) + cos (x y) (y + x \frac{d y}{d x}) x)

Simplify

- (1 \cdot sin (x y) + cos (x y) (y + x \frac{d y}{d x}) x) : - sin (x y) - x cos (x y) y - x^{2} cos (x y) \frac{d y}{d x}

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

x \to 0 lim (\frac{( x )}{x + 1})

\int e^{\frac{1}{x}} \cdot x^{- 2} d x

\frac{d}{d x} (x - 4 3 x)

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

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

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