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Popular >

derivative of x^2sqrt(3-x)

Solution

\frac{d}{d x} (x^{2} 3 - x)

Solution

\frac{- 5 x ^{2} + 12 x}{2 3 - x}

Solution steps

\frac{d}{d x} (x^{2} 3 - x)

Apply the Product Rule:

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

f = x^{2}, g = 3 - x

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

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

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

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

Simplify

2 x 3 - x + (- \frac{1}{2 3 - x}) x^{2} : \frac{- 5 x ^{2} + 12 x}{2 3 - x}

= \frac{- 5 x ^{2} + 12 x}{2 3 - x}

Popular Examples

integral of 1/(5+x^2)

\int \frac{1}{5 + x ^{2}} d x

integral of (ln(y))/(log_{10)(y)}

\int \frac{ln ( y )}{lo g _{10} ( y )} d y

tangent of f(x)=x^4-17x^2+16 tangent of

f (x) = x^{4} - 17 x^{2} + 16

integral of pi((sin(x))/x)^2

\int π (\frac{sin ( x )}{x})^{2} d x

limit as x approaches pi/2 of 3sin(x)

x \to \frac{π}{2} lim (3 sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(3-x) ?
The derivative of x^2sqrt(3-x) is (-5x^2+12x)/(2sqrt(3-x))
What is the first derivative of x^2sqrt(3-x) ?
The first derivative of x^2sqrt(3-x) is (-5x^2+12x)/(2sqrt(3-x))