What is the derivative of-xsin(x) ?

The derivative of-xsin(x) is -sin(x)-xcos(x)

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

The first derivative of-xsin(x) is -sin(x)-xcos(x)

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derivative of

- x sin (x)

- sin (x) - x cos (x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

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

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

= - (1 \cdot sin (x) + cos (x) x)

Simplify

- (1 \cdot sin (x) + cos (x) x) : - sin (x) - x cos (x)

= - sin (x) - x cos (x)

(x^{4} - y^{2}) d x (x^{3} - 2 x y) d y = 0

\int - 56 sin (7 z - 5) d z

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

\int \frac{1}{x ^{5} \cdot x ^{2} - 1} d x

\frac{\partial}{\partial x} (4 x y)

What is the derivative of-xsin(x) ?
The derivative of-xsin(x) is -sin(x)-xcos(x)
What is the first derivative of-xsin(x) ?
The first derivative of-xsin(x) is -sin(x)-xcos(x)