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Popular >

derivative of f(x)=xsqrt(3-x^2)

Solution

derivative of

f (x) = 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

integral of 3x-3

\int 3 x - 3 d x

limit as x approaches 3 of (2x-5)/(3x+4)

x \to 3 lim (\frac{2 x - 5}{3 x + 4})

derivative of x^{12}e^x derivative of

x^{12} e^{x}

derivative of f(x)=-x^2+2x derivative of

f (x) = - x^{2} + 2 x

derivative of f(x)= 1/10 x(x-2)(x-3)derivative of

f (x) = \frac{1}{10} x (x - 2) (x - 3)

Frequently Asked Questions (FAQ)

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