What is the derivative of sqrt(x)*cos(x) ?

The derivative of sqrt(x)*cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)

What is the first derivative of sqrt(x)*cos(x) ?

The first derivative of sqrt(x)*cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)

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\frac{d}{d x} (x \cdot cos (x))

\frac{cos ( x )}{2 x} - x sin (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} cos (x) + (- sin (x)) x

Simplify

\frac{1}{2 x} cos (x) + (- sin (x)) x : \frac{cos ( x )}{2 x} - x sin (x)

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

f (x) = 2 x 5 - 2 x, at x = - 1

\int r d r

y^{^{'}} = 1 + y^{2}

f (x) = 3 x^{2} - x + 3

\frac{d}{d x} (\frac{x - 17}{x - 17})

What is the derivative of sqrt(x)*cos(x) ?
The derivative of sqrt(x)*cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)
What is the first derivative of sqrt(x)*cos(x) ?
The first derivative of sqrt(x)*cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)