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Popular >

derivative of f(x)=xsqrt(3-x)

Solution

derivative of

f (x) = x 3 - x

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = 3 - x

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

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

\frac{d}{d x} (3 - x) = - \frac{1}{2 3 - x}

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

Simplify

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

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

Popular Examples

integral of 5xln(3-x)

\int 5 x ln (3 - x) d x

normal of y=(3x+1)^2,(0,1)normal of

y = (3 x + 1)^{2}, (0, 1)

derivative of f(x)=x^5 derivative of

f (x) = x^{5}

tangent of f(x)= 1/(x^4),(-2, 1/16)tangent of

f (x) = \frac{1}{x ^{4}}, (- 2, \frac{1}{16})

derivative of (c^2-x^2/(2x))

\frac{d}{d x} (\frac{c ^{2} - x ^{2}}{2 x})

Frequently Asked Questions (FAQ)

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