differentiate x^5 twice — step-by-step solution

1) Let's perform the differentiation:

\frac{d}{d x} (x^{5})

ⓘ The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{5})

5 x^{4}

5 x^{4}

2) Let's differentiate:

\frac{d}{d x} (5 x^{4})

ⓘ A constant factor stays in front of the derivative, (k*u)' = k*u':

\frac{d}{d x} (5 x^{4})

5 \cdot \frac{d}{d x} (x^{4})

■The derivative of x^n is n*x^(n-1):

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

4 x^{3}

5 \cdot 4 x^{3}

ⅰ

5 \cdot 4

20

▶Derivative:

20 x^{3}