Question

Replace ? with an expression that will make the equation valid.

Answer 1

4x³

Explanation:

d/dx ln(x⁴ + 7) = 1/(x⁴ + 7) × _?

To obtain the missing expression, let us simplify d/dx ln(x⁴ + 7). This can be obtained as follow:

Let y = ln (x⁴ + 7)

Let u = (x⁴ + 7)

Therefore,

ln(x⁴ + 7) = ln u

Thus,

y = ln u

dy/du = 1/u

Next, we shall determine du/dx. This is illustrated below:

u = (x⁴ + 7)

du/dx = 4x³

Finally, we shall determine dy/dx of ln (x⁴ + 7) as follow:

dy/dx = dy/du × du/dx

dy/du = 1/u

du/dx = 4x³

dy/dx = 1/u × 4x³

But:

u = (x⁴ + 7)

Therefore,

dy/dx = 1/(x⁴ + 7) × 4x³

Thus, the missing expression is 4x³