What is the derivative of x(x^2+x+1^3) ?

The derivative of x(x^2+x+1^3) is (x^2+x+1)^3+3x(x^2+x+1)^2(2x+1)

What is the first derivative of x(x^2+x+1^3) ?

The first derivative of x(x^2+x+1^3) is (x^2+x+1)^3+3x(x^2+x+1)^2(2x+1)

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Popular >

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

(x^{2} + x + 1)^{3} + 3 x (x^{2} + x + 1)^{2} (2 x + 1)

Solution steps

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

Apply the Product Rule:

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

f = x, g = (x^{2} + x + 1)^{3}

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

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

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

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

Simplify

= (x^{2} + x + 1)^{3} + 3 x (x^{2} + x + 1)^{2} (2 x + 1)

\frac{\partial}{\partial x} (\frac{1 + x}{x + y})

\int t^{2} + t d t

\int x - 2 y

- \frac{1}{s ( s - 1 ) ( 2 s + 1 ) ( s + 2 )}

\int_{0}^{7} 2 π x (7 x - x^{2}) d x

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