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).
Chain Rule – The chain rule is used to differentiate composite functions, which involves taking the derivative of the outer function and multiplying it by the derivative of the inner function.
Natural Logarithm Derivative – The derivative of the natural logarithm function ln(u) is 1/u * du/dx, where u is a function of x.
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