Calculus Examples

$y = x \cdot 4^{x}$

Step 1

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = x$ and $g (x) = 4^{x}$ .

$x \frac{d}{d x} [4^{x}] + 4^{x} \frac{d}{d x} [x]$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $4$ .

$x (4^{x} \ln (4)) + 4^{x} \frac{d}{d x} [x]$

Step 3

Differentiate using the Power Rule.

Tap for more steps...

Step 3.1

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

$x (4^{x} \ln (4)) + 4^{x} \cdot 1$

Step 3.2

Multiply $4^{x}$ by $1$ .

$x (4^{x} \ln (4)) + 4^{x}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Reorder terms.

$4^{x} x \ln (4) + 4^{x}$

Step 4.2

Reorder factors in $4^{x} x \ln (4) + 4^{x}$ .

$x \cdot 4^{x} \ln (4) + 4^{x}$