fifth derivative of x^5 — 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 perform the differentiation:

\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

20 x^{3}

3) Let's perform the differentiation:

\frac{d}{d x} (20 x^{3})

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

\frac{d}{d x} (20 x^{3})

20 \cdot \frac{d}{d x} (x^{3})

■The derivative of x^n is n*x^(n-1):

\frac{d}{d x} (x^{3})

3 x^{2}

20 \cdot 3 x^{2}

ⅰ

20 \cdot 3

60

60 x^{2}

4) Let's differentiate:

\frac{d}{d x} (60 x^{2})

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

\frac{d}{d x} (60 x^{2})

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

■The derivative of x^n is n*x^(n-1):

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

2 x

60 \cdot 2 x

ⅰ

60 \cdot 2

120

120 x

5) Let's perform the differentiation:

\frac{d}{d x} (120 x)

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

\frac{d}{d x} (120 x)

120

▶Derivative:

120