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Popular >

derivative of x^2sqrt(3-4x)

Solution

\frac{d}{d x} (x^{2} 3 - 4 x)

Solution

\frac{- 10 x ^{2} + 6 x}{3 - 4 x}

Solution steps

\frac{d}{d x} (x^{2} 3 - 4 x)

Apply the Product Rule:

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

f = x^{2}, g = 3 - 4 x

= \frac{d}{d x} (x^{2}) 3 - 4 x + \frac{d}{d x} (3 - 4 x) x^{2}

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

\frac{d}{d x} (3 - 4 x) = - \frac{2}{3 - 4 x}

= 2 x 3 - 4 x + (- \frac{2}{3 - 4 x}) x^{2}

Simplify

2 x 3 - 4 x + (- \frac{2}{3 - 4 x}) x^{2} : \frac{- 10 x ^{2} + 6 x}{3 - 4 x}

= \frac{- 10 x ^{2} + 6 x}{3 - 4 x}

Popular Examples

(\partial)/(\partial y)(3xe^{2xy})

\frac{\partial}{\partial y} (3 x e^{2 x y})

derivative of (3-2x^2^2sqrt(2x^2+1))

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

derivative of x/(x-4)derivative of

\frac{x}{x - 4}

derivative of (-2x^2+9)/(sqrt(9-x^2))derivative of

\frac{- 2 x ^{2} + 9}{9 - x ^{2}}

integral from 7 to 8 of (1/(x^2)-1)

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(3-4x) ?
The derivative of x^2sqrt(3-4x) is (-10x^2+6x)/(sqrt(3-4x))
What is the first derivative of x^2sqrt(3-4x) ?
The first derivative of x^2sqrt(3-4x) is (-10x^2+6x)/(sqrt(3-4x))