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Popular >

derivative of y=(x-1)(x^2+x+1)

Solution

derivative of

y = (x - 1) (x^{2} + x + 1)

Solution

3 x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x - 1, g = x^{2} + x + 1

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

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

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

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

Simplify

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

= 3 x^{2}

Popular Examples

(dy)/(dx)=(2x)/(y+1)

\frac{d y}{d x} = \frac{2 x}{y + 1}

integral from 1 to 1000 of (25)/(x^3)

\int_{1}^{1000} \frac{25}{x ^{3}} d x

x^2y^'+2xy=ln(x),y(1)=2

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 2

tangent of ((x^2))/(x+2)tangent of

\frac{( x ^{2} )}{x + 2}

limit as x approaches 0 of (cos(pi/2-x))/x

x \to 0 lim (\frac{cos ( \frac{π}{2} - x )}{x})

Frequently Asked Questions (FAQ)

What is the derivative of y=(x-1)(x^2+x+1) ?
The derivative of y=(x-1)(x^2+x+1) is 3x^2
What is the first derivative of y=(x-1)(x^2+x+1) ?
The first derivative of y=(x-1)(x^2+x+1) is 3x^2