What will be the differential function of log(x2 + 4)?a)2x/(x2 + 4) dxb)2x/(x2 – 4) dxc)-2x/(x2 + 4) dxd)-2x/(x2 – 4) dxCorrect answer is option 'A'. Can you explain this answer?

Question

What will be the differential function of log(x2 + 4)?a)2x/(x2 + 4) dxb)2x/(x2 &ndash; 4) dxc)-2x/(x2 + 4) dxd)-2x/(x2 &ndash; 4) dxCorrect answer is option 'A'. Can you explain this answer?

Answer

Explanation:

Given Function:
log(x^2 + 4)

Differential Function:
To find the differential function of log(x^2 + 4), we need to differentiate the given function with respect to x.

Steps to differentiate the function:
1. Let y = log(x^2 + 4)
2. Take exponential on both sides: e^y = x^2 + 4
3. Differentiate both sides with respect to x:
d/dx(e^y) = d/dx(x^2 + 4)
=> e^y(dy/dx) = 2x
4. Substitute e^y = x^2 + 4:
(x^2 + 4)(dy/dx) = 2x
5. Solve for dy/dx:
dy/dx = 2x / (x^2 + 4)

Final Answer:
The differential function of log(x^2 + 4) is 2x / (x^2 + 4) dx.

Answer

Let, y = f(x) = log(x² + 4)
So f(x) = log(x² + 4)
On differentiating it we get,
f’(x) = d/dx[log(x² + 4)]
So f’(x) = 2x/(x² + 4)
So the differential equation is:
dy = f’(x)dx
Hence, dy = 2x/(x² + 4) dx

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