differentiate (x^2+1)^3 — step-by-step solution

Let's perform the differentiation:

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

We differentiate using:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{n - 1}

(where f =

x^{2} + 1

)

ⓘ The derivative of

x^{n}

n x^{n - 1}

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

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

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

ⓘ The derivative of a sum is the sum of the derivatives:

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

\frac{d}{d x} (x^{2}) + 0

3 \cdot (\frac{d}{d x} (x^{2}) + 0) \cdot {(x^{2} + 1)}^{2}

ⓘ Adding 0 changes nothing:

\frac{d}{d x} (x^{2}) + 0

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

■Differentiating

x^{n}

gives

n x^{n - 1}

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

2 x

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

ⅰ

3 \cdot 2

6

▶Derivative:

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