Calculus Examples

$y = 4 t^{\frac{4}{3}}$

Step 1

Since $4$ is constant with respect to $t$ , the derivative of $4 t^{\frac{4}{3}}$ with respect to $t$ is $4 \frac{d}{d t} [t^{\frac{4}{3}}]$ .

$4 \frac{d}{d t} [t^{\frac{4}{3}}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d t} [t^{n}]$ is $n t^{n - 1}$ where $n = \frac{4}{3}$ .

$4 (\frac{4}{3} t^{\frac{4}{3} - 1})$

Step 3

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 (\frac{4}{3} t^{\frac{4}{3} - 1 \cdot \frac{3}{3}})$

Step 4

Combine $- 1$ and $\frac{3}{3}$ .

$4 (\frac{4}{3} t^{\frac{4}{3} + \frac{- 1 \cdot 3}{3}})$

Step 5

Combine the numerators over the common denominator.

$4 (\frac{4}{3} t^{\frac{4 - 1 \cdot 3}{3}})$

Step 6

Simplify the numerator.

Tap for more steps...

Step 6.1

Multiply $- 1$ by $3$ .

$4 (\frac{4}{3} t^{\frac{4 - 3}{3}})$

Step 6.2

Subtract $3$ from $4$ .

$4 (\frac{4}{3} t^{\frac{1}{3}})$

Step 7

Combine $\frac{4}{3}$ and $t^{\frac{1}{3}}$ .

$4 \frac{4 t^{\frac{1}{3}}}{3}$

Step 8

Combine $4$ and $\frac{4 t^{\frac{1}{3}}}{3}$ .

$\frac{4 (4 t^{\frac{1}{3}})}{3}$

Step 9

Multiply $4$ by $4$ .

$\frac{16 t^{\frac{1}{3}}}{3}$