What is the derivative of f(x)=xsqrt(4-x) ?

The derivative of f(x)=xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))

What is the first derivative of f(x)=xsqrt(4-x) ?

The first derivative of f(x)=xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))

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derivative of

f (x) = x 4 - x

\frac{- 3 x + 8}{2 4 - x}

Solution steps

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

Apply the Product Rule:

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

f = x, g = 4 - x

= \frac{d x}{d x} 4 - x + \frac{d}{d x} (4 - x) x

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

\frac{d}{d x} (4 - x) = - \frac{1}{2 4 - x}

= 1 \cdot 4 - x + (- \frac{1}{2 4 - x}) x

Simplify

1 \cdot 4 - x + (- \frac{1}{2 4 - x}) x : \frac{- 3 x + 8}{2 4 - x}

= \frac{- 3 x + 8}{2 4 - x}

\frac{d}{d x} (2 x + 3 y)

x \to 2 π lim (\frac{sin ( x )}{x})

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

n = 1 \sum \infty \frac{cos ( nπ )}{n}

t \to 0 lim (\frac{e ^{- 1 t} - 1}{t})

What is the derivative of f(x)=xsqrt(4-x) ?
The derivative of f(x)=xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))
What is the first derivative of f(x)=xsqrt(4-x) ?
The first derivative of f(x)=xsqrt(4-x) is (-3x+8)/(2sqrt(4-x))