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Popular >

derivative of 1/6 (2x+1^3)

Solution

\frac{d}{d x} (\frac{1}{6} (2 x + 1)^{3})

Solution

(2 x + 1)^{2}

Solution steps

\frac{d}{d x} (\frac{1}{6} (2 x + 1)^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} ((2 x + 1)^{3})

Apply the chain rule:

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

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

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

= \frac{1}{6} \cdot 3 (2 x + 1)^{2} \cdot 2

Simplify

\frac{1}{6} \cdot 3 (2 x + 1)^{2} \cdot 2 : (2 x + 1)^{2}

= (2 x + 1)^{2}

Popular Examples

derivative of (x-sqrt(x)/(x^{1/4)})

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

limit as x approaches-2 of (5x+7)^4

x \to - 2 lim ((5 x + 7)^{4})

derivative of 2^{x^2-3}derivative of

2^{x^{2} - 3}

integral from-infinity to 20 of re^{r/5}

\int_{- \infty}^{20} r e^{\frac{r}{5}} d r

integral of (sqrt(2x+1))/(x+1)

\int \frac{2 x + 1}{x + 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of 1/6 (2x+1^3) ?
The derivative of 1/6 (2x+1^3) is (2x+1)^2
What is the first derivative of 1/6 (2x+1^3) ?
The first derivative of 1/6 (2x+1^3) is (2x+1)^2