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Popular >

derivative of 4x^3+1/(x^2-x+3)

Solution

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}} - x + 3)

Solution

12 x^{2} - \frac{2}{x ^{3}} - 1

Solution steps

\frac{d}{d x} (4 x^{3} + \frac{1}{x ^{2}} - x + 3)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (\frac{1}{x ^{2}}) - \frac{d x}{d x} + \frac{d}{d x} (3)

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

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

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

\frac{d}{d x} (3) = 0

= 12 x^{2} - \frac{2}{x ^{3}} - 1 + 0

Simplify

= 12 x^{2} - \frac{2}{x ^{3}} - 1

Popular Examples

derivative of (5x/((x^3-6)^2))

\frac{d}{d x} (\frac{5 x}{( x ^{3} - 6 ) ^{2}})

(\partial)/(\partial x)(3/(2x^2))

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

y^{2} y^{^{'}} = x^{2}

integral from 0 to pi/3 of xsin(12x)

\int_{0}^{\frac{π}{3}} x sin (12 x) d x

integral of x^{2/3}

\int x^{\frac{2}{3}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 4x^3+1/(x^2-x+3) ?
The derivative of 4x^3+1/(x^2-x+3) is 12x^2-2/(x^3)-1
What is the first derivative of 4x^3+1/(x^2-x+3) ?
The first derivative of 4x^3+1/(x^2-x+3) is 12x^2-2/(x^3)-1