If y = ln(5x^2 + 3), find dy/dx at x = 1.

If y = ln(5x^2 + 3), find dy/dx at x = 1.

Correct Answer: 5/4

Step 1: Identify the function y = ln(5x^2 + 3).
Step 2: Use the chain rule to find the derivative dy/dx. The derivative of ln(u) is (1/u) * (du/dx), where u = 5x^2 + 3.
Step 3: Calculate du/dx. Since u = 5x^2 + 3, the derivative du/dx = 10x.
Step 4: Substitute u and du/dx into the derivative formula: dy/dx = (1/(5x^2 + 3)) * (10x).
Step 5: Simplify the expression: dy/dx = (10x)/(5x^2 + 3).
Step 6: Now, substitute x = 1 into the derivative: dy/dx = (10(1))/(5(1)^2 + 3).
Step 7: Calculate the denominator: 5(1)^2 + 3 = 5 + 3 = 8.
Step 8: Now, calculate dy/dx at x = 1: dy/dx = 10/8.
Step 9: Simplify 10/8 to get 5/4.

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