Calculus Examples

$f (x) = \frac{0.64 t - 18.99}{0.00054 t^{2} - 0.04594 t + 1}$

Step 1

Factor $0.01$ out of $0.64 t - 18.99$ .

Tap for more steps...

Step 1.1

Factor $0.01$ out of $0.64 t$ .

$\frac{d}{d x} [\frac{0.01 (64 t) - 18.99}{0.00054 t^{2} - 0.04594 t + 1}]$

Step 1.2

Factor $0.01$ out of $- 18.99$ .

$\frac{d}{d x} [\frac{0.01 (64 t) + 0.01 (- 1899)}{0.00054 t^{2} - 0.04594 t + 1}]$

Step 1.3

Factor $0.01$ out of $0.01 (64 t) + 0.01 (- 1899)$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00054 t^{2} - 0.04594 t + 1}]$

Step 2

Factor $0.00002$ out of $0.00054 t^{2} - 0.04594 t + 1$ .

Tap for more steps...

Step 2.1

Factor $0.00002$ out of $0.00054 t^{2}$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00002 (27 t^{2}) - 0.04594 t + 1}]$

Step 2.2

Factor $0.00002$ out of $- 0.04594 t$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00002 (27 t^{2}) + 0.00002 (- 2297 t) + 1}]$

Step 2.3

Factor $0.00002$ out of $1$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00002 (27 t^{2}) + 0.00002 (- 2297 t) + 0.00002 (50000)}]$

Step 2.4

Factor $0.00002$ out of $0.00002 (27 t^{2}) + 0.00002 (- 2297 t)$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00002 (27 t^{2} - 2297 t) + 0.00002 (50000)}]$

Step 2.5

Factor $0.00002$ out of $0.00002 (27 t^{2} - 2297 t) + 0.00002 (50000)$ .

$\frac{d}{d x} [\frac{0.01 (64 t - 1899)}{0.00002 (27 t^{2} - 2297 t + 50000)}]$

Step 3

Separate fractions.

$\frac{d}{d x} [\frac{0.01}{0.00002} \cdot \frac{64 t - 1899}{27 t^{2} - 2297 t + 50000}]$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Divide $0.01$ by $0.00002$ .

$\frac{d}{d x} [500 \frac{64 t - 1899}{27 t^{2} - 2297 t + 50000}]$

Step 4.2

Combine $500$ and $\frac{64 t - 1899}{27 t^{2} - 2297 t + 50000}$ .

$\frac{d}{d x} [\frac{500 (64 t - 1899)}{27 t^{2} - 2297 t + 50000}]$

Step 5

Since $\frac{500 (64 t - 1899)}{27 t^{2} - 2297 t + 50000}$ is constant with respect to $x$ , the derivative of $\frac{500 (64 t - 1899)}{27 t^{2} - 2297 t + 50000}$ with respect to $x$ is $0$ .

$0$