Calculus Examples

$f (x) = 3 t^{5} - 5 t^{3}$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Find the first derivative.

Tap for more steps...

Step 1.1.1

By the Sum Rule, the derivative of $3 t^{5} - 5 t^{3}$ with respect to $x$ is $\frac{d}{d x} [3 t^{5}] + \frac{d}{d x} [- 5 t^{3}]$ .

$\frac{d}{d x} [3 t^{5}] + \frac{d}{d x} [- 5 t^{3}]$

Step 1.1.2

Since $3 t^{5}$ is constant with respect to $x$ , the derivative of $3 t^{5}$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- 5 t^{3}]$

Step 1.1.3

Since $- 5 t^{3}$ is constant with respect to $x$ , the derivative of $- 5 t^{3}$ with respect to $x$ is $0$ .

$0 + 0$

Step 1.1.4

Add $0$ and $0$ .

$f' (x) = 0$

Step 1.2

The first derivative of $f (x)$ with respect to $x$ is $0$ .

$0$

Step 2

Set the first derivative equal to $0$ then solve the equation $0 = 0$ .

Tap for more steps...

Step 2.1

Set the first derivative equal to $0$ .

$0 = 0$

Step 2.2

Since $0 = 0$ , the equation will always be true.

Always true

Step 3

There are no values of $x$ in the domain of the original problem where the derivative is $0$ or undefined.

No critical points found