What is the derivative of xcos(sqrt(x-3)) ?

The derivative of xcos(sqrt(x-3)) is cos(sqrt(x-3))-(xsin(sqrt(x-3)))/(2sqrt(x-3))

What is the first derivative of xcos(sqrt(x-3)) ?

The first derivative of xcos(sqrt(x-3)) is cos(sqrt(x-3))-(xsin(sqrt(x-3)))/(2sqrt(x-3))

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derivative of

x cos (x - 3)

cos (x - 3) - \frac{x sin ( x - 3 )}{2 x - 3}

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x - 3)

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

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

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

= 1 \cdot cos (x - 3) + (- \frac{sin ( x - 3 )}{2 x - 3}) x

Simplify

1 \cdot cos (x - 3) + (- \frac{sin ( x - 3 )}{2 x - 3}) x : cos (x - 3) - \frac{x sin ( x - 3 )}{2 x - 3}

= cos (x - 3) - \frac{x sin ( x - 3 )}{2 x - 3}

What is the derivative of xcos(sqrt(x-3)) ?
The derivative of xcos(sqrt(x-3)) is cos(sqrt(x-3))-(xsin(sqrt(x-3)))/(2sqrt(x-3))
What is the first derivative of xcos(sqrt(x-3)) ?
The first derivative of xcos(sqrt(x-3)) is cos(sqrt(x-3))-(xsin(sqrt(x-3)))/(2sqrt(x-3))