What is the derivative of xsqrt(6-x) ?

The derivative of xsqrt(6-x) is (-3x+12)/(2sqrt(6-x))

What is the first derivative of xsqrt(6-x) ?

The first derivative of xsqrt(6-x) is (-3x+12)/(2sqrt(6-x))

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\frac{d}{d x} (x 6 - x)

\frac{- 3 x + 12}{2 6 - x}

Solution steps

\frac{d}{d x} (x 6 - x)

Apply the Product Rule:

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

f = x, g = 6 - x

= \frac{d x}{d x} 6 - x + \frac{d}{d x} (6 - x) x

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

\frac{d}{d x} (6 - x) = - \frac{1}{2 6 - x}

= 1 \cdot 6 - x + (- \frac{1}{2 6 - x}) x

Simplify

1 \cdot 6 - x + (- \frac{1}{2 6 - x}) x : \frac{- 3 x + 12}{2 6 - x}

= \frac{- 3 x + 12}{2 6 - x}

4 x d y - y d x = x^{2} d y

\int 4 cos (x) sin (x) d x

5 x - \frac{3}{x}

\frac{d}{d x} (5 \cdot cos (x))

4 \frac{d y}{d x} = y^{2}

What is the derivative of xsqrt(6-x) ?
The derivative of xsqrt(6-x) is (-3x+12)/(2sqrt(6-x))
What is the first derivative of xsqrt(6-x) ?
The first derivative of xsqrt(6-x) is (-3x+12)/(2sqrt(6-x))