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Popular >

derivative of xsqrt(3-x^2)

Solution

derivative of

x 3 - x^{2}

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of 1/(|2-x|)

x \to 2 lim (\frac{1}{∣ 2 - x ∣})

area y=-x^2+8x-12,y=x^2-8x+18,x=3x=6 area

y = - x^{2} + 8 x - 12, y = x^{2} - 8 x + 18, x = 3 x = 6

tangent of f(x)=6x^2+4x-7,-3 tangent of

f (x) = 6 x^{2} + 4 x - 7, - 3

integral of ((arcsin(x/3))^2)/(sqrt(9-x^2))

\int \frac{( arcsin ( \frac{x}{3} ) ) ^{2}}{9 - x ^{2}} d x

(\partial)/(\partial y)((x-y)^5)

\frac{\partial}{\partial y} ((x - y)^{5})

Frequently Asked Questions (FAQ)

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