Precalculus Examples

$\frac{(4 x + 1) (7^{x} \ln (7)) - 7^{x} \cdot 4}{{(4 x + 1)}^{2}}$

Step 1

Factor $7^{x}$ out of $(4 x + 1) \cdot 7^{x} \ln (7) - 7^{x} \cdot 4$ .

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Step 1.1

Factor $7^{x}$ out of $(4 x + 1) \cdot 7^{x} \ln (7)$ .

$\frac{7^{x} ((4 x + 1) \ln (7)) - 7^{x} \cdot 4}{{(4 x + 1)}^{2}}$

Step 1.2

Factor $7^{x}$ out of $- 7^{x} \cdot 4$ .

$\frac{7^{x} ((4 x + 1) \ln (7)) + 7^{x} (- 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 1.3

Factor $7^{x}$ out of $7^{x} ((4 x + 1) \ln (7)) + 7^{x} (- 1 \cdot 4)$ .

$\frac{7^{x} ((4 x + 1) \ln (7) - 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 2

Apply the distributive property.

$\frac{7^{x} (4 x \ln (7) + 1 \ln (7) - 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 3

Simplify $4 \ln (7)$ by moving $4$ inside the logarithm.

$\frac{7^{x} (x \ln (7^{4}) + 1 \ln (7) - 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 4

Multiply $\ln (7)$ by $1$ .

$\frac{7^{x} (x \ln (7^{4}) + \ln (7) - 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 5

Raise $7$ to the power of $4$ .

$\frac{7^{x} (x \ln (2401) + \ln (7) - 1 \cdot 4)}{{(4 x + 1)}^{2}}$

Step 6

Multiply $- 1$ by $4$ .

$\frac{7^{x} (x \ln (2401) + \ln (7) - 4)}{{(4 x + 1)}^{2}}$