If y = ln(5x^2 + 3), find dy/dx.
Correct Answer: dy/dx = (10x)/(5x^2 + 3)
- Step 1: Identify the function y = ln(5x^2 + 3). This is a natural logarithm function.
- Step 2: Recall the derivative of ln(u) is 1/u * du/dx, where u is a function of x.
- Step 3: In our case, u = 5x^2 + 3. We need to find du/dx.
- Step 4: Differentiate u = 5x^2 + 3. The derivative du/dx = 10x.
- Step 5: Now apply the chain rule: dy/dx = (1/(5x^2 + 3)) * (du/dx).
- Step 6: Substitute du/dx into the equation: dy/dx = (1/(5x^2 + 3)) * (10x).
- Step 7: Simplify the expression: dy/dx = (10x)/(5x^2 + 3).
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